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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 198208c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 198208.f1 | 198208c1 | \([0, 0, 0, -211, 1176]\) | \(16232712768/58843\) | \(3765952\) | \([2]\) | \(32448\) | \(0.12275\) | \(\Gamma_0(N)\)-optimal |
| 198208.f2 | 198208c2 | \([0, 0, 0, -116, 2240]\) | \(-42144192/504811\) | \(-2067705856\) | \([2]\) | \(64896\) | \(0.46932\) |
Rank
sage: E.rank()
The elliptic curves in class 198208c have rank \(0\).
Complex multiplication
The elliptic curves in class 198208c do not have complex multiplication.Modular form 198208.2.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.
