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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 24336x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24336.b2 | 24336x1 | \([0, 0, 0, -540462, 146660735]\) | \(141150208/6561\) | \(811535868185254992\) | \([2]\) | \(479232\) | \(2.1977\) | \(\Gamma_0(N)\)-optimal |
| 24336.b1 | 24336x2 | \([0, 0, 0, -8548527, 9620201630]\) | \(34909201168/81\) | \(160303381369926912\) | \([2]\) | \(958464\) | \(2.5443\) |
Rank
sage: E.rank()
The elliptic curves in class 24336x have rank \(1\).
Complex multiplication
The elliptic curves in class 24336x do not have complex multiplication.Modular form 24336.2.a.x
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 Cremona 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 Cremona labels.
