Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 400710bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.bb2 | 400710bb1 | \([1, 1, 1, 45659, 10268363]\) | \(223759095911/1094104800\) | \(-51473124222328800\) | \([]\) | \(5171040\) | \(1.8889\) | \(\Gamma_0(N)\)-optimal* |
400710.bb1 | 400710bb2 | \([1, 1, 1, -2558956, 1576483469]\) | \(-39390416456458249/56832000000\) | \(-2673711508992000000\) | \([]\) | \(15513120\) | \(2.4382\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 400710bb have rank \(1\).
Complex multiplication
The elliptic curves in class 400710bb do not have complex multiplication.Modular form 400710.2.a.bb
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.