Show commands:
SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 79350dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.du2 | 79350dl1 | \([1, 0, 0, -165588, 46913292]\) | \(-217081801/285660\) | \(-660748938308437500\) | \([2]\) | \(1824768\) | \(2.1122\) | \(\Gamma_0(N)\)-optimal |
79350.du1 | 79350dl2 | \([1, 0, 0, -3207338, 2209597542]\) | \(1577505447721/838350\) | \(1939154492861718750\) | \([2]\) | \(3649536\) | \(2.4588\) |
Rank
sage: E.rank()
The elliptic curves in class 79350dl have rank \(0\).
Complex multiplication
The elliptic curves in class 79350dl do not have complex multiplication.Modular form 79350.2.a.dl
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.