Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 131196a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
131196.j2 | 131196a1 | \([0, 1, 0, -4485, 102384]\) | \(1048576/117\) | \(1113509256912\) | \([2]\) | \(290304\) | \(1.0445\) | \(\Gamma_0(N)\)-optimal |
131196.j1 | 131196a2 | \([0, 1, 0, -17100, -755436]\) | \(3631696/507\) | \(77203308479232\) | \([2]\) | \(580608\) | \(1.3911\) |
Rank
sage: E.rank()
The elliptic curves in class 131196a have rank \(0\).
Complex multiplication
The elliptic curves in class 131196a do not have complex multiplication.Modular form 131196.2.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.