Properties

Label 245025l
Number of curves $2$
Conductor $245025$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 245025l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
245025.l2 245025l1 \([0, 0, 1, -54450, -4866469]\) \(884736/5\) \(100895935078125\) \([]\) \(777600\) \(1.5290\) \(\Gamma_0(N)\)-optimal
245025.l1 245025l2 \([0, 0, 1, -326700, 68504906]\) \(2359296/125\) \(204314268533203125\) \([]\) \(2332800\) \(2.0783\)  

Rank

sage: E.rank()
 

The elliptic curves in class 245025l have rank \(0\).

Complex multiplication

The elliptic curves in class 245025l do not have complex multiplication.

Modular form 245025.2.a.l

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + 2 q^{7} - 4 q^{13} + 4 q^{16} - 6 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.