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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 50430w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50430.x2 | 50430w1 | \([1, 0, 0, -896, -7824]\) | \(1154320649/291600\) | \(20097363600\) | \([2]\) | \(46080\) | \(0.68679\) | \(\Gamma_0(N)\)-optimal |
50430.x1 | 50430w2 | \([1, 0, 0, -4996, 129116]\) | \(200098975049/10628820\) | \(732548903220\) | \([2]\) | \(92160\) | \(1.0334\) |
Rank
sage: E.rank()
The elliptic curves in class 50430w have rank \(1\).
Complex multiplication
The elliptic curves in class 50430w do not have complex multiplication.Modular form 50430.2.a.w
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.