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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 36414.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36414.g1 | 36414o2 | \([1, -1, 0, -3390891, -2506434427]\) | \(-31403829411/1605632\) | \(-220459429129386295296\) | \([]\) | \(1762560\) | \(2.6638\) | |
36414.g2 | 36414o1 | \([1, -1, 0, 220164, -7825104]\) | \(6266230821/3764768\) | \(-709076926520244576\) | \([3]\) | \(587520\) | \(2.1145\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36414.g have rank \(1\).
Complex multiplication
The elliptic curves in class 36414.g do not have complex multiplication.Modular form 36414.2.a.g
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.