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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 22050cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.j2 | 22050cb1 | \([1, -1, 0, -24117, 6336791]\) | \(-189/2\) | \(-16416171597656250\) | \([]\) | \(161280\) | \(1.7935\) | \(\Gamma_0(N)\)-optimal |
22050.j1 | 22050cb2 | \([1, -1, 0, -75269742, -251331415084]\) | \(-5745702166029/8192\) | \(-67240638864000000000\) | \([]\) | \(2096640\) | \(3.0760\) |
Rank
sage: E.rank()
The elliptic curves in class 22050cb have rank \(1\).
Complex multiplication
The elliptic curves in class 22050cb do not have complex multiplication.Modular form 22050.2.a.cb
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.