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Properties

Label 25350.z
Number of curves $2$
Conductor $25350$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 25350.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.z1 25350bb2 \([1, 0, 1, -3601901, -2631442552]\) \(68523370149961/243360\) \(18353941222500000\) \([2]\) \(645120\) \(2.3390\)  
25350.z2 25350bb1 \([1, 0, 1, -221901, -42362552]\) \(-16022066761/998400\) \(-75298220400000000\) \([2]\) \(322560\) \(1.9925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25350.z have rank \(0\).

Complex multiplication

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

Modular form 25350.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 2 q^{7} - q^{8} + q^{9} - 4 q^{11} + q^{12} + 2 q^{14} + q^{16} - 4 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.