Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 302016l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302016.l1 | 302016l1 | \([0, -1, 0, -805271617, -8795261564351]\) | \(-124352595912593543977/103332962304\) | \(-47988249993474616590336\) | \([]\) | \(71884800\) | \(3.6555\) | \(\Gamma_0(N)\)-optimal |
302016.l2 | 302016l2 | \([0, -1, 0, -625107457, -12834522865151]\) | \(-58169016237585194137/119573538788081664\) | \(-55530440084410267273135128576\) | \([]\) | \(215654400\) | \(4.2048\) |
Rank
sage: E.rank()
The elliptic curves in class 302016l have rank \(1\).
Complex multiplication
The elliptic curves in class 302016l do not have complex multiplication.Modular form 302016.2.a.l
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.