Properties

Label 925.b
Number of curves $3$
Conductor $925$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 925.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
925.b1 925b3 \([0, -1, 1, -46833, -3885432]\) \(727057727488000/37\) \(578125\) \([]\) \(864\) \(1.0268\)  
925.b2 925b2 \([0, -1, 1, -583, -5057]\) \(1404928000/50653\) \(791453125\) \([]\) \(288\) \(0.47749\)  
925.b3 925b1 \([0, -1, 1, -83, 318]\) \(4096000/37\) \(578125\) \([]\) \(96\) \(-0.071812\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 925.b have rank \(1\).

Complex multiplication

The elliptic curves in class 925.b do not have complex multiplication.

Modular form 925.2.a.b

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.