Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 115920i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.ds1 | 115920i1 | \([0, 0, 0, -87, 86]\) | \(10536048/5635\) | \(38949120\) | \([2]\) | \(30720\) | \(0.14774\) | \(\Gamma_0(N)\)-optimal |
115920.ds2 | 115920i2 | \([0, 0, 0, 333, 674]\) | \(147704148/92575\) | \(-2559513600\) | \([2]\) | \(61440\) | \(0.49432\) |
Rank
sage: E.rank()
The elliptic curves in class 115920i have rank \(0\).
Complex multiplication
The elliptic curves in class 115920i 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 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.