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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 35131.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35131.b1 | 35131c3 | \([0, -1, 1, -1422497, 653492395]\) | \(-50357871050752/19\) | \(-120105897931\) | \([]\) | \(243810\) | \(1.9140\) | |
| 35131.b2 | 35131c2 | \([0, -1, 1, -17257, 934070]\) | \(-89915392/6859\) | \(-43358229153091\) | \([]\) | \(81270\) | \(1.3647\) | |
| 35131.b3 | 35131c1 | \([0, -1, 1, 1233, 325]\) | \(32768/19\) | \(-120105897931\) | \([]\) | \(27090\) | \(0.81543\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35131.b have rank \(0\).
Complex multiplication
The elliptic curves in class 35131.b do not have complex multiplication.Modular form 35131.2.a.b
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
