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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 476100.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476100.m1 | 476100m1 | \([0, 0, 0, -1708246800, -27175044688875]\) | \(62200479744/625\) | \(5539388724308785781250000\) | \([2]\) | \(198402048\) | \(3.9069\) | \(\Gamma_0(N)\)-optimal |
476100.m2 | 476100m2 | \([0, 0, 0, -1667183175, -28543572119250]\) | \(-3613864464/390625\) | \(-55393887243087857812500000000\) | \([2]\) | \(396804096\) | \(4.2535\) |
Rank
sage: E.rank()
The elliptic curves in class 476100.m have rank \(1\).
Complex multiplication
The elliptic curves in class 476100.m do not have complex multiplication.Modular form 476100.2.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 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.