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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 129360.eq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.eq1 | 129360gd2 | \([0, 1, 0, -21003621, -700462254381]\) | \(-2126464142970105856/438611057788643355\) | \(-211362415975530914088529920\) | \([]\) | \(57600000\) | \(3.7306\) | |
129360.eq2 | 129360gd1 | \([0, 1, 0, -7009221, 8362172979]\) | \(-79028701534867456/16987307596875\) | \(-8186018821999603200000\) | \([]\) | \(11520000\) | \(2.9259\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.eq have rank \(0\).
Complex multiplication
The elliptic curves in class 129360.eq do not have complex multiplication.Modular form 129360.2.a.eq
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.