Properties

Label 92575.m
Number of curves $3$
Conductor $92575$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 92575.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92575.m1 92575n3 \([0, -1, 1, -1736883, 922243293]\) \(-250523582464/13671875\) \(-31623877655029296875\) \([]\) \(1710720\) \(2.4999\)  
92575.m2 92575n1 \([0, -1, 1, -17633, -993957]\) \(-262144/35\) \(-80957126796875\) \([]\) \(190080\) \(1.4013\) \(\Gamma_0(N)\)-optimal
92575.m3 92575n2 \([0, -1, 1, 114617, 2510668]\) \(71991296/42875\) \(-99172480326171875\) \([]\) \(570240\) \(1.9506\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92575.m have rank \(1\).

Complex multiplication

The elliptic curves in class 92575.m do not have complex multiplication.

Modular form 92575.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.