Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 57960bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57960.g2 | 57960bo1 | \([0, 0, 0, 771117, -150738082]\) | \(67929287623001276/52460218164375\) | \(-39161343018833280000\) | \([2]\) | \(1376256\) | \(2.4476\) | \(\Gamma_0(N)\)-optimal |
57960.g1 | 57960bo2 | \([0, 0, 0, -3609003, -1297453498]\) | \(3481993537261218002/1527951821484375\) | \(2281219845861600000000\) | \([2]\) | \(2752512\) | \(2.7941\) |
Rank
sage: E.rank()
The elliptic curves in class 57960bo have rank \(0\).
Complex multiplication
The elliptic curves in class 57960bo do not have complex multiplication.Modular form 57960.2.a.bo
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.