Properties

Label 331240.d
Number of curves $2$
Conductor $331240$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 331240.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
331240.d1 331240d1 \([0, 1, 0, -3944516, -2790476480]\) \(46689225424/3901625\) \(567196894846583456000\) \([2]\) \(18579456\) \(2.7242\) \(\Gamma_0(N)\)-optimal
331240.d2 331240d2 \([0, 1, 0, 4170864, -12782132336]\) \(13799183324/129390625\) \(-75240404418424336000000\) \([2]\) \(37158912\) \(3.0708\)  

Rank

sage: E.rank()
 

The elliptic curves in class 331240.d have rank \(1\).

Complex multiplication

The elliptic curves in class 331240.d do not have complex multiplication.

Modular form 331240.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{9} - 6 q^{11} + 2 q^{15} + 2 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.