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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 328560c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328560.c2 | 328560c1 | \([0, -1, 0, -52686421, 152599016221]\) | \(-1539038632738816/66363694875\) | \(-697430362274223939072000\) | \([]\) | \(41368320\) | \(3.3409\) | \(\Gamma_0(N)\)-optimal |
| 328560.c1 | 328560c2 | \([0, -1, 0, -4310824021, 108941733943261]\) | \(-843013059301831868416/61543395\) | \(-646772792733772001280\) | \([]\) | \(124104960\) | \(3.8902\) |
Rank
sage: E.rank()
The elliptic curves in class 328560c have rank \(0\).
Complex multiplication
The elliptic curves in class 328560c do not have complex multiplication.Modular form 328560.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
