Properties

Label 25200.l
Number of curves $4$
Conductor $25200$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 25200.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.l1 25200bf4 \([0, 0, 0, -67275, 6716250]\) \(1443468546/7\) \(163296000000\) \([2]\) \(65536\) \(1.3520\)  
25200.l2 25200bf3 \([0, 0, 0, -13275, -465750]\) \(11090466/2401\) \(56010528000000\) \([2]\) \(65536\) \(1.3520\)  
25200.l3 25200bf2 \([0, 0, 0, -4275, 101250]\) \(740772/49\) \(571536000000\) \([2, 2]\) \(32768\) \(1.0054\)  
25200.l4 25200bf1 \([0, 0, 0, 225, 6750]\) \(432/7\) \(-20412000000\) \([2]\) \(16384\) \(0.65884\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25200.l have rank \(2\).

Complex multiplication

The elliptic curves in class 25200.l do not have complex multiplication.

Modular form 25200.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{7} - 4q^{11} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.