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Properties

Label 114240.jn
Number of curves $2$
Conductor $114240$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("jn1")
 
E.isogeny_class()
 

Elliptic curves in class 114240.jn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114240.jn1 114240ej2 \([0, 1, 0, -1169902945, 14889257918975]\) \(675512349748162449958490329/25568496800736303750000\) \(6702628025332217610240000000\) \([2]\) \(82575360\) \(4.1077\)  
114240.jn2 114240ej1 \([0, 1, 0, 30097055, 837017918975]\) \(11501534367688741509671/1161179873437500000000\) \(-304396336742400000000000000\) \([2]\) \(41287680\) \(3.7611\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 114240.2.a.jn

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.