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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 304200.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304200.cu1 | 304200cu1 | \([0, 0, 0, -24766950, -44570264375]\) | \(1909913257984/129730653\) | \(114122231463551483250000\) | \([2]\) | \(25804800\) | \(3.1729\) | \(\Gamma_0(N)\)-optimal |
| 304200.cu2 | 304200cu2 | \([0, 0, 0, 21433425, -191718458750]\) | \(77366117936/1172914587\) | \(-16508743540768566828000000\) | \([2]\) | \(51609600\) | \(3.5195\) |
Rank
sage: E.rank()
The elliptic curves in class 304200.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 304200.cu do not have complex multiplication.Modular form 304200.2.a.cu
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.
