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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 193200.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.w1 | 193200hk2 | \([0, -1, 0, -10025008, -6003387488]\) | \(3481993537261218002/1527951821484375\) | \(48894458287500000000000\) | \([2]\) | \(16515072\) | \(3.0496\) | |
| 193200.w2 | 193200hk1 | \([0, -1, 0, 2141992, -698575488]\) | \(67929287623001276/52460218164375\) | \(-839363490630000000000\) | \([2]\) | \(8257536\) | \(2.7030\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193200.w have rank \(1\).
Complex multiplication
The elliptic curves in class 193200.w do not have complex multiplication.Modular form 193200.2.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 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.
