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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 116688.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.c1 | 116688d2 | \([0, -1, 0, -1405404, -640645200]\) | \(1199188932400332409552/367460647585317\) | \(94069925781841152\) | \([2]\) | \(1806336\) | \(2.2338\) | |
| 116688.c2 | 116688d1 | \([0, -1, 0, -76219, -12738206]\) | \(-3060547801156175872/2627414297644851\) | \(-42038628762317616\) | \([2]\) | \(903168\) | \(1.8873\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116688.c have rank \(1\).
Complex multiplication
The elliptic curves in class 116688.c do not have complex multiplication.Modular form 116688.2.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.
