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Properties

Label 476850jd
Number of curves $2$
Conductor $476850$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("jd1")
 
E.isogeny_class()
 

Elliptic curves in class 476850jd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.jd1 476850jd1 \([1, 0, 0, -740713, 249759917]\) \(-119168121961/2524500\) \(-952113952195312500\) \([]\) \(9953280\) \(2.2402\) \(\Gamma_0(N)\)-optimal
476850.jd2 476850jd2 \([1, 0, 0, 3052412, 1125971792]\) \(8339492177639/6277634880\) \(-2367606954262605000000\) \([]\) \(29859840\) \(2.7895\)  

Rank

sage: E.rank()
 

The elliptic curves in class 476850jd have rank \(0\).

Complex multiplication

The elliptic curves in class 476850jd do not have complex multiplication.

Modular form 476850.2.a.jd

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + q^{11} + q^{12} + q^{13} - q^{14} + q^{16} + q^{18} - 7 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.