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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 950e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 950.d2 | 950e1 | \([1, 1, 1, -388, 2781]\) | \(-413493625/152\) | \(-2375000\) | \([]\) | \(288\) | \(0.19128\) | \(\Gamma_0(N)\)-optimal |
| 950.d3 | 950e2 | \([1, 1, 1, 237, 11281]\) | \(94196375/3511808\) | \(-54872000000\) | \([]\) | \(864\) | \(0.74058\) | |
| 950.d1 | 950e3 | \([1, 1, 1, -2138, -306969]\) | \(-69173457625/2550136832\) | \(-39845888000000\) | \([]\) | \(2592\) | \(1.2899\) |
Rank
sage: E.rank()
The elliptic curves in class 950e have rank \(1\).
Complex multiplication
The elliptic curves in class 950e do not have complex multiplication.Modular form 950.2.a.e
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 Cremona 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 Cremona labels.
