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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 834g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
834.g2 | 834g1 | \([1, 0, 0, -70, 356]\) | \(-37966934881/34587648\) | \(-34587648\) | \([5]\) | \(400\) | \(0.14336\) | \(\Gamma_0(N)\)-optimal |
834.g1 | 834g2 | \([1, 0, 0, -1090, -40504]\) | \(-143228059472161/622666136388\) | \(-622666136388\) | \([]\) | \(2000\) | \(0.94808\) |
Rank
sage: E.rank()
The elliptic curves in class 834g have rank \(1\).
Complex multiplication
The elliptic curves in class 834g do not have complex multiplication.Modular form 834.2.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.