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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 159120.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.c1 | 159120cp2 | \([0, 0, 0, -31563, 1546938]\) | \(43132764843/12138425\) | \(978618856550400\) | \([2]\) | \(786432\) | \(1.5834\) | |
159120.c2 | 159120cp1 | \([0, 0, 0, 5157, 158922]\) | \(188132517/244205\) | \(-19688190013440\) | \([2]\) | \(393216\) | \(1.2368\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159120.c have rank \(1\).
Complex multiplication
The elliptic curves in class 159120.c do not have complex multiplication.Modular form 159120.2.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.