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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2064.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2064.c1 | 2064e2 | \([0, -1, 0, -958416, 361505472]\) | \(-23769846831649063249/3261823333284\) | \(-13360428373131264\) | \([]\) | \(28224\) | \(2.1121\) | |
| 2064.c2 | 2064e1 | \([0, -1, 0, 2544, -111168]\) | \(444369620591/1540767744\) | \(-6310984679424\) | \([]\) | \(4032\) | \(1.1391\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2064.c have rank \(0\).
Complex multiplication
The elliptic curves in class 2064.c do not have complex multiplication.Modular form 2064.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
