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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 63426f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63426.b2 | 63426f1 | \([1, 1, 0, -164831, -22726011]\) | \(558051585337/73066752\) | \(64847011358714112\) | \([2]\) | \(737280\) | \(1.9541\) | \(\Gamma_0(N)\)-optimal |
63426.b1 | 63426f2 | \([1, 1, 0, -2548111, -1566614795]\) | \(2061621066895417/43751664\) | \(38829762849875184\) | \([2]\) | \(1474560\) | \(2.3007\) |
Rank
sage: E.rank()
The elliptic curves in class 63426f have rank \(1\).
Complex multiplication
The elliptic curves in class 63426f do not have complex multiplication.Modular form 63426.2.a.f
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.