Properties

Label 25200.ev
Number of curves 4
Conductor 25200
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("25200.ev1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200.ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.ev1 25200ei4 [0, 0, 0, -405075, -99224750] [2] 196608  
25200.ev2 25200ei2 [0, 0, 0, -27075, -1322750] [2, 2] 98304  
25200.ev3 25200ei1 [0, 0, 0, -9075, 315250] [2] 49152 \(\Gamma_0(N)\)-optimal
25200.ev4 25200ei3 [0, 0, 0, 62925, -8252750] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 25200.ev have rank \(0\).

Modular form 25200.2.a.ev

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.