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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 380880ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380880.ei2 | 380880ei1 | \([0, 0, 0, 157113, -337050234]\) | \(574992/66125\) | \(-49324643945149536000\) | \([2]\) | \(7299072\) | \(2.4581\) | \(\Gamma_0(N)\)-optimal |
380880.ei1 | 380880ei2 | \([0, 0, 0, -6413067, -6049164726]\) | \(9776035692/359375\) | \(1072274868372816000000\) | \([2]\) | \(14598144\) | \(2.8047\) |
Rank
sage: E.rank()
The elliptic curves in class 380880ei have rank \(1\).
Complex multiplication
The elliptic curves in class 380880ei do not have complex multiplication.Modular form 380880.2.a.ei
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.