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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 476850m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.m1 | 476850m1 | \([1, 1, 0, -1315100, 4092115950]\) | \(-16673509288825/469998676422\) | \(-7090390926277936323750\) | \([]\) | \(39564288\) | \(2.8732\) | \(\Gamma_0(N)\)-optimal |
476850.m2 | 476850m2 | \([1, 1, 0, 11798275, -108543907275]\) | \(12039422435197175/344379193347288\) | \(-5195297838490315664295000\) | \([]\) | \(118692864\) | \(3.4226\) |
Rank
sage: E.rank()
The elliptic curves in class 476850m have rank \(0\).
Complex multiplication
The elliptic curves in class 476850m do not have complex multiplication.Modular form 476850.2.a.m
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 Cremona 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 Cremona labels.