↑

Properties

Label 25350ci
Number of curves $2$
Conductor $25350$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 25350ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.cn1 25350ci1 \([1, 1, 1, -1540646338, -23276331036769]\) \(-134057911417971280740025/1872\) \(-5647366530000\) \([]\) \(5644800\) \(3.4265\) \(\Gamma_0(N)\)-optimal
25350.cn2 25350ci2 \([1, 1, 1, -1501155263, -24526004080219]\) \(-198417696411528597145/22989483914821632\) \(-43346034322428237004800000000\) \([]\) \(28224000\) \(4.2312\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25350ci have rank \(1\).

Complex multiplication

The elliptic curves in class 25350ci do not have complex multiplication.

Modular form 25350.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 3 q^{7} + q^{8} + q^{9} + 3 q^{11} - q^{12} + 3 q^{14} + q^{16} - 3 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.