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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 439569.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.i1 | 439569i2 | \([1, -1, 1, -5150732177, -142281237679460]\) | \(177930109857804849/634933\) | \(53927348833368462095397\) | \([2]\) | \(371589120\) | \(4.0036\) | |
439569.i2 | 439569i1 | \([1, -1, 1, -322066712, -2220967201670]\) | \(43499078731809/82055753\) | \(6969316787465324189622777\) | \([2]\) | \(185794560\) | \(3.6570\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569.i have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.i do not have complex multiplication.Modular form 439569.2.a.i
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.