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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2925c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2925.m2 | 2925c1 | \([1, -1, 0, -5442, 173591]\) | \(-57960603/8125\) | \(-2498818359375\) | \([2]\) | \(4608\) | \(1.1102\) | \(\Gamma_0(N)\)-optimal |
| 2925.m1 | 2925c2 | \([1, -1, 0, -89817, 10382966]\) | \(260549802603/4225\) | \(1299385546875\) | \([2]\) | \(9216\) | \(1.4568\) |
Rank
sage: E.rank()
The elliptic curves in class 2925c have rank \(0\).
Complex multiplication
The elliptic curves in class 2925c do not have complex multiplication.Modular form 2925.2.a.c
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.
