Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 115920.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.i1 | 115920cw2 | \([0, 0, 0, -106203, -23798]\) | \(44365623586201/25674468750\) | \(76663552896000000\) | \([2]\) | \(884736\) | \(1.9293\) | |
115920.i2 | 115920cw1 | \([0, 0, 0, -73083, -7581782]\) | \(14457238157881/49990500\) | \(149270833152000\) | \([2]\) | \(442368\) | \(1.5827\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.i have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.i do not have complex multiplication.Modular form 115920.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.