Show commands:
SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 379050ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.ds2 | 379050ds1 | \([1, 0, 1, 220924, 3268298]\) | \(2595575/1512\) | \(-694661836640625000\) | \([]\) | \(7464960\) | \(2.1129\) | \(\Gamma_0(N)\)-optimal |
379050.ds1 | 379050ds2 | \([1, 0, 1, -3163451, 2291105798]\) | \(-7620530425/526848\) | \(-242051057745000000000\) | \([]\) | \(22394880\) | \(2.6623\) |
Rank
sage: E.rank()
The elliptic curves in class 379050ds have rank \(1\).
Complex multiplication
The elliptic curves in class 379050ds do not have complex multiplication.Modular form 379050.2.a.ds
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.