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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 3150.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.q1 | 3150s1 | \([1, -1, 0, -38367, -2867459]\) | \(4386781853/27216\) | \(38750906250000\) | \([2]\) | \(12800\) | \(1.4454\) | \(\Gamma_0(N)\)-optimal |
| 3150.q2 | 3150s2 | \([1, -1, 0, -15867, -6219959]\) | \(-310288733/11573604\) | \(-16478822882812500\) | \([2]\) | \(25600\) | \(1.7919\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.q have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.q do not have complex multiplication.Modular form 3150.2.a.q
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.
