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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 132496y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132496.bc1 | 132496y1 | \([0, -1, 0, -2188944, -1310539712]\) | \(-226981/14\) | \(-71542875972718911488\) | \([]\) | \(3594240\) | \(2.5642\) | \(\Gamma_0(N)\)-optimal |
| 132496.bc2 | 132496y2 | \([0, -1, 0, 6423296, 79513610240]\) | \(5735339/537824\) | \(-2748391123367969703723008\) | \([]\) | \(17971200\) | \(3.3689\) |
Rank
sage: E.rank()
The elliptic curves in class 132496y have rank \(0\).
Complex multiplication
The elliptic curves in class 132496y do not have complex multiplication.Modular form 132496.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
