Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 152592.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.bg1 | 152592cg1 | \([0, -1, 0, -41712, 1606080]\) | \(81182737/35904\) | \(3549738096132096\) | \([2]\) | \(663552\) | \(1.6795\) | \(\Gamma_0(N)\)-optimal |
152592.bg2 | 152592cg2 | \([0, -1, 0, 143248, 11815872]\) | \(3288008303/2517768\) | \(-248925383991263232\) | \([2]\) | \(1327104\) | \(2.0261\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.bg do not have complex multiplication.Modular form 152592.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.