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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 59840.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59840.z1 | 59840j4 | \([0, 0, 0, -8012, 276016]\) | \(1735787669832/116875\) | \(3829760000\) | \([2]\) | \(92160\) | \(0.89394\) | |
| 59840.z2 | 59840j3 | \([0, 0, 0, -2732, -51696]\) | \(68820189192/4593655\) | \(150524887040\) | \([2]\) | \(92160\) | \(0.89394\) | |
| 59840.z3 | 59840j2 | \([0, 0, 0, -532, 3744]\) | \(4065356736/874225\) | \(3580825600\) | \([2, 2]\) | \(46080\) | \(0.54737\) | |
| 59840.z4 | 59840j1 | \([0, 0, 0, 73, 356]\) | \(672221376/1244485\) | \(-79647040\) | \([2]\) | \(23040\) | \(0.20079\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59840.z have rank \(0\).
Complex multiplication
The elliptic curves in class 59840.z do not have complex multiplication.Modular form 59840.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
