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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 71148v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71148.l2 | 71148v1 | \([0, -1, 0, 15811, -427986]\) | \(131072/99\) | \(-330141050060976\) | \([2]\) | \(259200\) | \(1.4740\) | \(\Gamma_0(N)\)-optimal |
| 71148.l1 | 71148v2 | \([0, -1, 0, -73124, -3594072]\) | \(810448/363\) | \(19368274936910592\) | \([2]\) | \(518400\) | \(1.8206\) |
Rank
sage: E.rank()
The elliptic curves in class 71148v have rank \(0\).
Complex multiplication
The elliptic curves in class 71148v do not have complex multiplication.Modular form 71148.2.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 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.
