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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 188760.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.cp1 | 188760h2 | \([0, 1, 0, -35491760, 81372242400]\) | \(1362762798430761362/10456875\) | \(37939183476480000\) | \([2]\) | \(6881280\) | \(2.7739\) | |
| 188760.cp2 | 188760h1 | \([0, 1, 0, -2216760, 1272662400]\) | \(-664085303622724/1843359375\) | \(-3343998543600000000\) | \([2]\) | \(3440640\) | \(2.4273\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 188760.cp do not have complex multiplication.Modular form 188760.2.a.cp
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.
