Properties

Label 114240jq
Number of curves $4$
Conductor $114240$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jq1")
 
E.isogeny_class()
 

Elliptic curves in class 114240jq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114240.ji4 114240jq1 \([0, 1, 0, 895, -17025]\) \(302111711/669375\) \(-175472640000\) \([2]\) \(131072\) \(0.84172\) \(\Gamma_0(N)\)-optimal
114240.ji3 114240jq2 \([0, 1, 0, -7105, -191425]\) \(151334226289/28676025\) \(7517247897600\) \([2, 2]\) \(262144\) \(1.1883\)  
114240.ji2 114240jq3 \([0, 1, 0, -34305, 2262015]\) \(17032120495489/1339001685\) \(351011257712640\) \([2]\) \(524288\) \(1.5349\)  
114240.ji1 114240jq4 \([0, 1, 0, -107905, -13678465]\) \(530044731605089/26309115\) \(6896776642560\) \([2]\) \(524288\) \(1.5349\)  

Rank

sage: E.rank()
 

The elliptic curves in class 114240jq have rank \(0\).

Complex multiplication

The elliptic curves in class 114240jq do not have complex multiplication.

Modular form 114240.2.a.jq

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} + 6 q^{13} + q^{15} - q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.