Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 53130l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53130.n2 | 53130l1 | \([1, 1, 0, 908, -7856]\) | \(82648257725879/77119257600\) | \(-77119257600\) | \([2]\) | \(64000\) | \(0.77627\) | \(\Gamma_0(N)\)-optimal |
53130.n1 | 53130l2 | \([1, 1, 0, -4692, -76176]\) | \(11427266093672521/4233227533920\) | \(4233227533920\) | \([2]\) | \(128000\) | \(1.1228\) |
Rank
sage: E.rank()
The elliptic curves in class 53130l have rank \(0\).
Complex multiplication
The elliptic curves in class 53130l do not have complex multiplication.Modular form 53130.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.