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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 14490.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.z1 | 14490bb7 | \([1, -1, 0, -2285091144, 39448430519400]\) | \(1810117493172631097464564372609/125368453502655029296875000\) | \(91393602603435516357421875000\) | \([6]\) | \(15925248\) | \(4.3050\) | |
| 14490.z2 | 14490bb6 | \([1, -1, 0, -2245670064, 40961041011648]\) | \(1718043013877225552292911401729/9180538178765625000000\) | \(6692612332320140625000000\) | \([2, 6]\) | \(7962624\) | \(3.9585\) | |
| 14490.z3 | 14490bb3 | \([1, -1, 0, -2245667184, 40961151325440]\) | \(1718036403880129446396978632449/49057344000000\) | \(35762803776000000\) | \([6]\) | \(3981312\) | \(3.6119\) | |
| 14490.z4 | 14490bb8 | \([1, -1, 0, -2206295064, 42466591386648]\) | \(-1629247127728109256861881401729/125809119536174660320875000\) | \(-91714848141871327373917875000\) | \([6]\) | \(15925248\) | \(4.3050\) | |
| 14490.z5 | 14490bb4 | \([1, -1, 0, -425852784, -3370791981312]\) | \(11715873038622856702991202049/46415372499833400000000\) | \(33836806552378548600000000\) | \([2]\) | \(5308416\) | \(3.7557\) | |
| 14490.z6 | 14490bb2 | \([1, -1, 0, -39541104, 3795068160]\) | \(9378698233516887309850369/5418996968417034240000\) | \(3950448789976017960960000\) | \([2, 2]\) | \(2654208\) | \(3.4092\) | |
| 14490.z7 | 14490bb1 | \([1, -1, 0, -27744624, 56107738368]\) | \(3239908336204082689644289/9880281924658790400\) | \(7202725523076258201600\) | \([2]\) | \(1327104\) | \(3.0626\) | \(\Gamma_0(N)\)-optimal |
| 14490.z8 | 14490bb5 | \([1, -1, 0, 158026896, 30229666560]\) | \(598672364899527954087397631/346996861747253448998400\) | \(-252960712213747764319833600\) | \([2]\) | \(5308416\) | \(3.7557\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.z have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.z do not have complex multiplication.Modular form 14490.2.a.z
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.
