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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 24336.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24336.cf1 | 24336q1 | \([0, 0, 0, -990678, 356562115]\) | \(1909913257984/129730653\) | \(7303822813667294928\) | \([2]\) | \(645120\) | \(2.3682\) | \(\Gamma_0(N)\)-optimal |
| 24336.cf2 | 24336q2 | \([0, 0, 0, 857337, 1533747670]\) | \(77366117936/1172914587\) | \(-1056559586609188276992\) | \([2]\) | \(1290240\) | \(2.7147\) |
Rank
sage: E.rank()
The elliptic curves in class 24336.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 24336.cf do not have complex multiplication.Modular form 24336.2.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.
