Show commands:
SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 111573bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111573.v1 | 111573bl1 | \([0, 0, 1, -8526, 330223]\) | \(-799178752/86779\) | \(-7442698214259\) | \([]\) | \(165888\) | \(1.2079\) | \(\Gamma_0(N)\)-optimal |
111573.v2 | 111573bl2 | \([0, 0, 1, 53214, -426092]\) | \(194305753088/113359939\) | \(-9722442244826619\) | \([]\) | \(497664\) | \(1.7572\) |
Rank
sage: E.rank()
The elliptic curves in class 111573bl have rank \(1\).
Complex multiplication
The elliptic curves in class 111573bl do not have complex multiplication.Modular form 111573.2.a.bl
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.