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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 127400.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 127400.cf1 | 127400br1 | \([0, -1, 0, -583508, -158496988]\) | \(46689225424/3901625\) | \(1836089118500000000\) | \([2]\) | \(2654208\) | \(2.2465\) | \(\Gamma_0(N)\)-optimal |
| 127400.cf2 | 127400br2 | \([0, -1, 0, 616992, -727533988]\) | \(13799183324/129390625\) | \(-243562842250000000000\) | \([2]\) | \(5308416\) | \(2.5930\) |
Rank
sage: E.rank()
The elliptic curves in class 127400.cf have rank \(1\).
Complex multiplication
The elliptic curves in class 127400.cf do not have complex multiplication.Modular form 127400.2.a.cf
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.
