Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 170c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
170.e2 | 170c1 | \([1, 0, 0, 399, -919]\) | \(7023836099951/4456448000\) | \(-4456448000\) | \([3]\) | \(84\) | \(0.54047\) | \(\Gamma_0(N)\)-optimal |
170.e1 | 170c2 | \([1, 0, 0, -6641, -215575]\) | \(-32391289681150609/1228250000000\) | \(-1228250000000\) | \([]\) | \(252\) | \(1.0898\) |
Rank
sage: E.rank()
The elliptic curves in class 170c have rank \(0\).
Complex multiplication
The elliptic curves in class 170c do not have complex multiplication.Modular form 170.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.