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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 97104.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97104.a1 | 97104br2 | \([0, -1, 0, -10500, 416556]\) | \(20720464/63\) | \(389290712832\) | \([2]\) | \(236544\) | \(1.0926\) | |
| 97104.a2 | 97104br1 | \([0, -1, 0, -385, 11956]\) | \(-16384/147\) | \(-56771562288\) | \([2]\) | \(118272\) | \(0.74605\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97104.a have rank \(0\).
Complex multiplication
The elliptic curves in class 97104.a do not have complex multiplication.Modular form 97104.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
