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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 574.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
574.g1 | 574i2 | \([1, -1, 1, -9611313, -11466507927]\) | \(98191033604529537629349729/10906239337336\) | \(10906239337336\) | \([]\) | \(24696\) | \(2.3707\) | |
574.g2 | 574i1 | \([1, -1, 1, -19353, 958713]\) | \(801581275315909089/70810888830976\) | \(70810888830976\) | \([7]\) | \(3528\) | \(1.3978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 574.g have rank \(1\).
Complex multiplication
The elliptic curves in class 574.g do not have complex multiplication.Modular form 574.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.