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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 47096.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47096.c1 | 47096k2 | \([0, 1, 0, -30081168, 63490179616]\) | \(2471097448795250/98942809\) | \(120531948008342915072\) | \([2]\) | \(2580480\) | \(2.9361\) | |
| 47096.c2 | 47096k1 | \([0, 1, 0, -1789928, 1091020672]\) | \(-1041220466500/242597383\) | \(-147765842966496197632\) | \([2]\) | \(1290240\) | \(2.5896\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47096.c have rank \(1\).
Complex multiplication
The elliptic curves in class 47096.c do not have complex multiplication.Modular form 47096.2.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.
