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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 25200ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.ba1 | 25200ey1 | \([0, 0, 0, -613875, 184131250]\) | \(4386781853/27216\) | \(158723712000000000\) | \([2]\) | \(307200\) | \(2.1385\) | \(\Gamma_0(N)\)-optimal |
| 25200.ba2 | 25200ey2 | \([0, 0, 0, -253875, 398331250]\) | \(-310288733/11573604\) | \(-67497258528000000000\) | \([2]\) | \(614400\) | \(2.4851\) |
Rank
sage: E.rank()
The elliptic curves in class 25200ey have rank \(0\).
Complex multiplication
The elliptic curves in class 25200ey do not have complex multiplication.Modular form 25200.2.a.ey
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.
