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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 950.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 950.a1 | 950b2 | \([1, 1, 0, -69500, -7081250]\) | \(-2376117230685121/342950\) | \(-5358593750\) | \([]\) | \(1728\) | \(1.2759\) | |
| 950.a2 | 950b1 | \([1, 1, 0, -750, -12500]\) | \(-2992209121/2375000\) | \(-37109375000\) | \([]\) | \(576\) | \(0.72655\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 950.a have rank \(0\).
Complex multiplication
The elliptic curves in class 950.a do not have complex multiplication.Modular form 950.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
