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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 30492.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30492.a1 | 30492h2 | \([0, 0, 0, -722007, 202325310]\) | \(4662947952/717409\) | \(6404042263719082752\) | \([2]\) | \(691200\) | \(2.3321\) | |
30492.a2 | 30492h1 | \([0, 0, 0, 78408, 17429445]\) | \(95551488/290521\) | \(-162085780435038768\) | \([2]\) | \(345600\) | \(1.9856\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30492.a have rank \(0\).
Complex multiplication
The elliptic curves in class 30492.a do not have complex multiplication.Modular form 30492.2.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.