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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 101430.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.s1 | 101430bi8 | \([1, -1, 0, -111969466065, -13530587729222075]\) | \(1810117493172631097464564372609/125368453502655029296875000\) | \(10752365952691585063934326171875000\) | \([2]\) | \(764411904\) | \(5.2780\) | |
| 101430.s2 | 101430bi6 | \([1, -1, 0, -110037833145, -14049416991328979]\) | \(1718043013877225552292911401729/9180538178765625000000\) | \(787379148285132224390625000000\) | \([2, 2]\) | \(382205952\) | \(4.9314\) | |
| 101430.s3 | 101430bi3 | \([1, -1, 0, -110037692025, -14049454829241875]\) | \(1718036403880129446396978632449/49057344000000\) | \(4207458101442624000000\) | \([2]\) | \(191102976\) | \(4.5848\) | |
| 101430.s4 | 101430bi7 | \([1, -1, 0, -108108458145, -14565824628703979]\) | \(-1629247127728109256861881401729/125809119536174660320875000\) | \(-10790160169043019794214064075875000\) | \([2]\) | \(764411904\) | \(5.2780\) | |
| 101430.s5 | 101430bi5 | \([1, -1, 0, -20866786425, 1156223383162861]\) | \(11715873038622856702991202049/46415372499833400000000\) | \(3980866454080783864241400000000\) | \([2]\) | \(254803968\) | \(4.7287\) | |
| 101430.s6 | 101430bi2 | \([1, -1, 0, -1937514105, -1297833350675]\) | \(9378698233516887309850369/5418996968417034240000\) | \(464766349691888537088983040000\) | \([2, 2]\) | \(127401984\) | \(4.3821\) | |
| 101430.s7 | 101430bi1 | \([1, -1, 0, -1359486585, -19242235287059]\) | \(3239908336204082689644289/9880281924658790400\) | \(847393455064398701160038400\) | \([2]\) | \(63700992\) | \(4.0355\) | \(\Gamma_0(N)\)-optimal |
| 101430.s8 | 101430bi4 | \([1, -1, 0, 7743317895, -10384262265875]\) | \(598672364899527954087397631/346996861747253448998400\) | \(-29760574831235210724464103206400\) | \([2]\) | \(254803968\) | \(4.7287\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.s have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.s do not have complex multiplication.Modular form 101430.2.a.s
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
