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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1008.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1008.c1 | 1008b1 | \([0, 0, 0, -6, -5]\) | \(55296/7\) | \(3024\) | \([2]\) | \(64\) | \(-0.60292\) | \(\Gamma_0(N)\)-optimal |
| 1008.c2 | 1008b2 | \([0, 0, 0, 9, -26]\) | \(11664/49\) | \(-338688\) | \([2]\) | \(128\) | \(-0.25635\) |
Rank
sage: E.rank()
The elliptic curves in class 1008.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1008.c do not have complex multiplication.Modular form 1008.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
