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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 35280fc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.fw1 | 35280fc1 | \([0, 0, 0, -8967, 327026]\) | \(-177953104/125\) | \(-56010528000\) | \([]\) | \(51840\) | \(0.99869\) | \(\Gamma_0(N)\)-optimal |
| 35280.fw2 | 35280fc2 | \([0, 0, 0, 8673, 1388954]\) | \(161017136/1953125\) | \(-875164500000000\) | \([]\) | \(155520\) | \(1.5480\) |
Rank
sage: E.rank()
The elliptic curves in class 35280fc have rank \(0\).
Complex multiplication
The elliptic curves in class 35280fc do not have complex multiplication.Modular form 35280.2.a.fc
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.
