Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 10608e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10608.s1 | 10608e1 | \([0, 1, 0, -14288, -659868]\) | \(315042014258500/1262881737\) | \(1293190898688\) | \([2]\) | \(15360\) | \(1.1806\) | \(\Gamma_0(N)\)-optimal |
10608.s2 | 10608e2 | \([0, 1, 0, -7528, -1279084]\) | \(-23040414103250/330419182041\) | \(-676698484819968\) | \([2]\) | \(30720\) | \(1.5272\) |
Rank
sage: E.rank()
The elliptic curves in class 10608e have rank \(0\).
Complex multiplication
The elliptic curves in class 10608e do not have complex multiplication.Modular form 10608.2.a.e
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.