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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 75900be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75900.bi2 | 75900be1 | \([0, 1, 0, -2333, -42912]\) | \(5619712000/184437\) | \(46109250000\) | \([2]\) | \(82944\) | \(0.81956\) | \(\Gamma_0(N)\)-optimal |
75900.bi1 | 75900be2 | \([0, 1, 0, -5708, 105588]\) | \(5142706000/1728243\) | \(6912972000000\) | \([2]\) | \(165888\) | \(1.1661\) |
Rank
sage: E.rank()
The elliptic curves in class 75900be have rank \(1\).
Complex multiplication
The elliptic curves in class 75900be do not have complex multiplication.Modular form 75900.2.a.be
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.