Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 143745w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
143745.bb2 | 143745w1 | \([1, 0, 1, 176572, 28646381]\) | \(237291625871/275349375\) | \(-706471163139144375\) | \([2]\) | \(1751040\) | \(2.1113\) | \(\Gamma_0(N)\)-optimal |
143745.bb1 | 143745w2 | \([1, 0, 1, -1021303, 271575431]\) | \(45917324980129/14146664175\) | \(36296469873051697575\) | \([2]\) | \(3502080\) | \(2.4578\) |
Rank
sage: E.rank()
The elliptic curves in class 143745w have rank \(0\).
Complex multiplication
The elliptic curves in class 143745w do not have complex multiplication.Modular form 143745.2.a.w
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.