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Properties

Label 25230.r
Number of curves $4$
Conductor $25230$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 25230.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25230.r1 25230o4 \([1, 1, 1, -440989721, -3564619432921]\) \(15944875212653044225849/1291776000000\) \(768378490308096000000\) \([2]\) \(7257600\) \(3.4521\)  
25230.r2 25230o3 \([1, 1, 1, -27621401, -55453090777]\) \(3918075806073018169/35030827008000\) \(20837152858275053568000\) \([2]\) \(3628800\) \(3.1056\)  
25230.r3 25230o2 \([1, 1, 1, -6011906, -3810409297]\) \(40399154288735689/12848183733600\) \(7642399317238131285600\) \([2]\) \(2419200\) \(2.9028\)  
25230.r4 25230o1 \([1, 1, 1, -2378786, 1366060079]\) \(2502660030961609/91031454720\) \(54147632212011525120\) \([2]\) \(1209600\) \(2.5563\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25230.r have rank \(0\).

Complex multiplication

The elliptic curves in class 25230.r do not have complex multiplication.

Modular form 25230.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} + 6 q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + q^{15} + q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.