Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 95139a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95139.j2 | 95139a1 | \([1, -1, 0, -14595, -122032]\) | \(19683/11\) | \(192156084484353\) | \([2]\) | \(362880\) | \(1.4310\) | \(\Gamma_0(N)\)-optimal |
95139.j1 | 95139a2 | \([1, -1, 0, -144330, 21024773]\) | \(19034163/121\) | \(2113716929327883\) | \([2]\) | \(725760\) | \(1.7776\) |
Rank
sage: E.rank()
The elliptic curves in class 95139a have rank \(0\).
Complex multiplication
The elliptic curves in class 95139a do not have complex multiplication.Modular form 95139.2.a.a
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.