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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 319725g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
319725.g2 | 319725g1 | \([0, 0, 1, -554925, -430878744]\) | \(-352558182400/1292202387\) | \(-69266991424956766875\) | \([]\) | \(12902400\) | \(2.4928\) | \(\Gamma_0(N)\)-optimal |
319725.g1 | 319725g2 | \([0, 0, 1, -20377875, 59039250156]\) | \(-27933450833920/28780659747\) | \(-964220916531652885546875\) | \([]\) | \(64512000\) | \(3.2975\) |
Rank
sage: E.rank()
The elliptic curves in class 319725g have rank \(1\).
Complex multiplication
The elliptic curves in class 319725g do not have complex multiplication.Modular form 319725.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.