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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 425880.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.e1 | 425880e2 | \([0, 0, 0, -4863463657923, -4128256050068337122]\) | \(803550333470755251060766154/90075015625\) | \(1426106625346814864544000000\) | \([2]\) | \(4692639744\) | \(5.5503\) | |
425880.e2 | 425880e1 | \([0, 0, 0, -303967251003, -64503656580653498]\) | \(392361552237381907701748/4154116321200125\) | \(32884883599623774711752462976000\) | \([2]\) | \(2346319872\) | \(5.2037\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 425880.e have rank \(1\).
Complex multiplication
The elliptic curves in class 425880.e do not have complex multiplication.Modular form 425880.2.a.e
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.