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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 115920m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.ec2 | 115920m1 | \([0, 0, 0, -198747, -19742886]\) | \(43075884983148/16573802875\) | \(334051493876352000\) | \([2]\) | \(958464\) | \(2.0616\) | \(\Gamma_0(N)\)-optimal |
115920.ec1 | 115920m2 | \([0, 0, 0, -2791827, -1794965454]\) | \(59699126465470854/19845765625\) | \(799998371424000000\) | \([2]\) | \(1916928\) | \(2.4082\) |
Rank
sage: E.rank()
The elliptic curves in class 115920m have rank \(1\).
Complex multiplication
The elliptic curves in class 115920m do not have complex multiplication.Modular form 115920.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.