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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 76230g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76230.p1 | 76230g1 | \([1, -1, 0, -5580240, 5064162560]\) | \(551105805571803/1376829440\) | \(48009540254477598720\) | \([2]\) | \(4300800\) | \(2.6539\) | \(\Gamma_0(N)\)-optimal |
76230.p2 | 76230g2 | \([1, -1, 0, -3489360, 8903436416]\) | \(-134745327251163/903920796800\) | \(-31519388400664257878400\) | \([2]\) | \(8601600\) | \(3.0004\) |
Rank
sage: E.rank()
The elliptic curves in class 76230g have rank \(1\).
Complex multiplication
The elliptic curves in class 76230g do not have complex multiplication.Modular form 76230.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.