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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 14490.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.a1 | 14490l5 | \([1, -1, 0, -762210, 256320126]\) | \(67176973097223766561/91487391870\) | \(66694308673230\) | \([2]\) | \(131072\) | \(1.9267\) | |
| 14490.a2 | 14490l3 | \([1, -1, 0, -48060, 3939516]\) | \(16840406336564161/604708416900\) | \(440832435920100\) | \([2, 2]\) | \(65536\) | \(1.5802\) | |
| 14490.a3 | 14490l2 | \([1, -1, 0, -7560, -167184]\) | \(65553197996161/20996010000\) | \(15306091290000\) | \([2, 2]\) | \(32768\) | \(1.2336\) | |
| 14490.a4 | 14490l1 | \([1, -1, 0, -6840, -216000]\) | \(48551226272641/9273600\) | \(6760454400\) | \([2]\) | \(16384\) | \(0.88702\) | \(\Gamma_0(N)\)-optimal |
| 14490.a5 | 14490l6 | \([1, -1, 0, 18090, 13901706]\) | \(898045580910239/115117148363070\) | \(-83920401156678030\) | \([2]\) | \(131072\) | \(1.9267\) | |
| 14490.a6 | 14490l4 | \([1, -1, 0, 21420, -1158300]\) | \(1490881681033919/1650501562500\) | \(-1203215639062500\) | \([2]\) | \(65536\) | \(1.5802\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.a have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.a do not have complex multiplication.Modular form 14490.2.a.a
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
