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Properties

Label 117325.l
Number of curves $2$
Conductor $117325$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 117325.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117325.l1 117325m2 \([0, -1, 1, -481333, 128330068]\) \(671088640/2197\) \(40374922092578125\) \([]\) \(1244160\) \(2.0518\)  
117325.l2 117325m1 \([0, -1, 1, -30083, -1855557]\) \(163840/13\) \(238904864453125\) \([]\) \(414720\) \(1.5025\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 117325.l have rank \(1\).

Complex multiplication

The elliptic curves in class 117325.l do not have complex multiplication.

Modular form 117325.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.