Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 19950.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19950.z1 | 19950s3 | \([1, 0, 1, -27401, 1712198]\) | \(145606291302529/2993062590\) | \(46766602968750\) | \([2]\) | \(73728\) | \(1.4135\) | |
| 19950.z2 | 19950s2 | \([1, 0, 1, -3651, -45302]\) | \(344324701729/143280900\) | \(2238764062500\) | \([2, 2]\) | \(36864\) | \(1.0669\) | |
| 19950.z3 | 19950s1 | \([1, 0, 1, -3151, -68302]\) | \(221335335649/95760\) | \(1496250000\) | \([2]\) | \(18432\) | \(0.72034\) | \(\Gamma_0(N)\)-optimal |
| 19950.z4 | 19950s4 | \([1, 0, 1, 12099, -328802]\) | \(12537291235391/10262778750\) | \(-160355917968750\) | \([2]\) | \(73728\) | \(1.4135\) |
Rank
sage: E.rank()
The elliptic curves in class 19950.z have rank \(1\).
Complex multiplication
The elliptic curves in class 19950.z do not have complex multiplication.Modular form 19950.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
