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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 457776t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.t2 | 457776t1 | \([0, 0, 0, 6936, -255476]\) | \(8192/11\) | \(-49551146447616\) | \([]\) | \(1105920\) | \(1.3136\) | \(\Gamma_0(N)\)-optimal |
| 457776.t1 | 457776t2 | \([0, 0, 0, -201144, -34921604]\) | \(-199794688/1331\) | \(-5995688720161536\) | \([]\) | \(3317760\) | \(1.8629\) |
Rank
sage: E.rank()
The elliptic curves in class 457776t have rank \(0\).
Complex multiplication
The elliptic curves in class 457776t do not have complex multiplication.Modular form 457776.2.a.t
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
