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Properties

Label 137280eq
Number of curves $2$
Conductor $137280$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("eq1")
 
E.isogeny_class()
 

Elliptic curves in class 137280eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137280.gu2 137280eq1 \([0, 1, 0, -64495425, -199778630625]\) \(-113180217375258301213009/260161419375000000\) \(-68199755120640000000000\) \([2]\) \(15482880\) \(3.2626\) \(\Gamma_0(N)\)-optimal
137280.gu1 137280eq2 \([0, 1, 0, -1032495425, -12770033030625]\) \(464352938845529653759213009/2445173327025000\) \(640987516639641600000\) \([2]\) \(30965760\) \(3.6092\)  

Rank

sage: E.rank()
 

The elliptic curves in class 137280eq have rank \(0\).

Complex multiplication

The elliptic curves in class 137280eq do not have complex multiplication.

Modular form 137280.2.a.eq

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} - q^{11} + q^{13} + q^{15} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.