Show commands:
SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 430950gw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.gw1 | 430950gw1 | \([1, 0, 0, -19540713, 31386435417]\) | \(4980061835533/313344000\) | \(51919628930208000000000\) | \([2]\) | \(60383232\) | \(3.1098\) | \(\Gamma_0(N)\)-optimal |
430950.gw2 | 430950gw2 | \([1, 0, 0, 15611287, 131886003417]\) | \(2539391358707/46818000000\) | \(-7757522681954906250000000\) | \([2]\) | \(120766464\) | \(3.4563\) |
Rank
sage: E.rank()
The elliptic curves in class 430950gw have rank \(1\).
Complex multiplication
The elliptic curves in class 430950gw do not have complex multiplication.Modular form 430950.2.a.gw
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.