Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 166635.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166635.v1 | 166635bd1 | \([0, 0, 1, -29118, 1912743]\) | \(-7079867613184/1250235\) | \(-482141875635\) | \([]\) | \(248832\) | \(1.2466\) | \(\Gamma_0(N)\)-optimal |
166635.v2 | 166635bd2 | \([0, 0, 1, 8142, 6359724]\) | \(154786758656/45397807875\) | \(-17507256026722875\) | \([]\) | \(746496\) | \(1.7959\) |
Rank
sage: E.rank()
The elliptic curves in class 166635.v have rank \(1\).
Complex multiplication
The elliptic curves in class 166635.v do not have complex multiplication.Modular form 166635.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.