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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 327990.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
327990.l1 | 327990l1 | \([1, 0, 1, -3343834, -2119930228]\) | \(285020220941/31150080\) | \(451898757719997419520\) | \([2]\) | \(14966784\) | \(2.6970\) | \(\Gamma_0(N)\)-optimal |
327990.l2 | 327990l2 | \([1, 0, 1, 4460646, -10542525044]\) | \(676604913139/3701505600\) | \(-53698282069696568366400\) | \([2]\) | \(29933568\) | \(3.0435\) |
Rank
sage: E.rank()
The elliptic curves in class 327990.l have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.l do not have complex multiplication.Modular form 327990.2.a.l
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.