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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 126350.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126350.v1 | 126350b2 | \([1, -1, 0, -9523067, -11545429659]\) | \(-46905074216911089/1146880000000\) | \(-2335352320000000000000\) | \([]\) | \(7112448\) | \(2.8855\) | |
126350.v2 | 126350b1 | \([1, -1, 0, -46817, 13068341]\) | \(-5573207889/32941720\) | \(-67078092064375000\) | \([]\) | \(1016064\) | \(1.9125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126350.v have rank \(1\).
Complex multiplication
The elliptic curves in class 126350.v do not have complex multiplication.Modular form 126350.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.