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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 126960y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.m2 | 126960y1 | \([0, -1, 0, -2073856, -1153777664]\) | \(-1626794704081/8125440\) | \(-4926901182120591360\) | \([2]\) | \(3041280\) | \(2.4342\) | \(\Gamma_0(N)\)-optimal |
| 126960.m1 | 126960y2 | \([0, -1, 0, -33221376, -73690122240]\) | \(6687281588245201/165600\) | \(100412388222566400\) | \([2]\) | \(6082560\) | \(2.7808\) |
Rank
sage: E.rank()
The elliptic curves in class 126960y have rank \(1\).
Complex multiplication
The elliptic curves in class 126960y do not have complex multiplication.Modular form 126960.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
