Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 720.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
720.i1 | 720b2 | \([0, 0, 0, -1107, -14094]\) | \(3721734/25\) | \(1007769600\) | \([2]\) | \(384\) | \(0.56230\) | |
720.i2 | 720b1 | \([0, 0, 0, -27, -486]\) | \(-108/5\) | \(-100776960\) | \([2]\) | \(192\) | \(0.21572\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 720.i have rank \(0\).
Complex multiplication
The elliptic curves in class 720.i do not have complex multiplication.Modular form 720.2.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.