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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 412090g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412090.g2 | 412090g1 | \([1, 0, 1, -42068, 124771098]\) | \(-49/40\) | \(-6720914628419277160\) | \([]\) | \(10160640\) | \(2.2917\) | \(\Gamma_0(N)\)-optimal* |
412090.g1 | 412090g2 | \([1, 0, 1, -20234478, 35033409506]\) | \(-5452947409/250\) | \(-42005716427620482250\) | \([]\) | \(30481920\) | \(2.8410\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 412090g have rank \(1\).
Complex multiplication
The elliptic curves in class 412090g do not have complex multiplication.Modular form 412090.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.