Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 64974.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64974.bw1 | 64974bx2 | \([1, 0, 0, -87674406, 422770263012]\) | \(-1521059241134755603512440881/695595284594977727840256\) | \(-34084168945153908664172544\) | \([7]\) | \(14620032\) | \(3.6057\) | |
64974.bw2 | 64974bx1 | \([1, 0, 0, -2226316, -1477144936]\) | \(-24905087205614147556241/4819348696095929736\) | \(-236148086108700557064\) | \([]\) | \(2088576\) | \(2.6328\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64974.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 64974.bw do not have complex multiplication.Modular form 64974.2.a.bw
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.