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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 25578v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25578.r2 | 25578v1 | \([1, -1, 0, 2196, 65232]\) | \(13651919/29696\) | \(-2546910729216\) | \([]\) | \(43200\) | \(1.0647\) | \(\Gamma_0(N)\)-optimal |
| 25578.r1 | 25578v2 | \([1, -1, 0, -200664, -34782588]\) | \(-10418796526321/82044596\) | \(-7036646747932116\) | \([]\) | \(216000\) | \(1.8694\) |
Rank
sage: E.rank()
The elliptic curves in class 25578v have rank \(0\).
Complex multiplication
The elliptic curves in class 25578v do not have complex multiplication.Modular form 25578.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
