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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 396.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
396.a1 | 396b2 | \([0, 0, 0, -111, 214]\) | \(810448/363\) | \(67744512\) | \([2]\) | \(96\) | \(0.19801\) | |
396.a2 | 396b1 | \([0, 0, 0, 24, 25]\) | \(131072/99\) | \(-1154736\) | \([2]\) | \(48\) | \(-0.14856\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 396.a have rank \(1\).
Complex multiplication
The elliptic curves in class 396.a do not have complex multiplication.Modular form 396.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.