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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 54208.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54208.v1 | 54208l1 | \([0, -1, 0, -43237, -3446089]\) | \(-78843215872/539\) | \(-61111768256\) | \([]\) | \(115200\) | \(1.2505\) | \(\Gamma_0(N)\)-optimal |
| 54208.v2 | 54208l2 | \([0, -1, 0, -23877, -6558209]\) | \(-13278380032/156590819\) | \(-17754252025501376\) | \([]\) | \(345600\) | \(1.7998\) | |
| 54208.v3 | 54208l3 | \([0, -1, 0, 213283, 169888831]\) | \(9463555063808/115539436859\) | \(-13099850259287481536\) | \([]\) | \(1036800\) | \(2.3491\) |
Rank
sage: E.rank()
The elliptic curves in class 54208.v have rank \(0\).
Complex multiplication
The elliptic curves in class 54208.v do not have complex multiplication.Modular form 54208.2.a.v
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
