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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 31878.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31878.n1 | 31878q2 | \([1, -1, 0, -274371542037, 55316825404416117]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-111955886374413312\) | \([3]\) | \(71850240\) | \(4.6638\) | |
| 31878.n2 | 31878q1 | \([1, -1, 0, -3387273237, 75882571232373]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-157297410096329008902832128\) | \([]\) | \(23950080\) | \(4.1145\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 31878.n have rank \(1\).
Complex multiplication
The elliptic curves in class 31878.n do not have complex multiplication.Modular form 31878.2.a.n
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.
