Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 380926bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380926.bj2 | 380926bj1 | \([1, 0, 0, -1128, -5552]\) | \(391197625/194672\) | \(78991862768\) | \([]\) | \(342144\) | \(0.78398\) | \(\Gamma_0(N)\)-optimal |
380926.bj1 | 380926bj2 | \([1, 0, 0, -74383, -7814535]\) | \(112167304419625/94208\) | \(38226685952\) | \([]\) | \(1026432\) | \(1.3333\) |
Rank
sage: E.rank()
The elliptic curves in class 380926bj have rank \(1\).
Complex multiplication
The elliptic curves in class 380926bj do not have complex multiplication.Modular form 380926.2.a.bj
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.