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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 439569.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.v1 | 439569v2 | \([1, -1, 1, -43086920, -83679766842]\) | \(104154702625/24649677\) | \(2093593702341600472236093\) | \([2]\) | \(49545216\) | \(3.3783\) | |
439569.v2 | 439569v1 | \([1, -1, 1, -14514935, 20185113030]\) | \(3981876625/232713\) | \(19765227400465363935417\) | \([2]\) | \(24772608\) | \(3.0317\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569.v have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.v do not have complex multiplication.Modular form 439569.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.