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Properties

Label 285090ce
Number of curves $2$
Conductor $285090$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 285090ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
285090.ce1 285090ce1 \([1, 0, 0, -186364200, 979307640000]\) \(-715832117907767882405148124801/65214833959432170000000\) \(-65214833959432170000000\) \([7]\) \(78675968\) \(3.4168\) \(\Gamma_0(N)\)-optimal
285090.ce2 285090ce2 \([1, 0, 0, 1244830950, -31268332431570]\) \(213331430131166950008878809576799/545828612088802939198075490730\) \(-545828612088802939198075490730\) \([]\) \(550731776\) \(4.3898\)  

Rank

sage: E.rank()
 

The elliptic curves in class 285090ce have rank \(0\).

Complex multiplication

The elliptic curves in class 285090ce do not have complex multiplication.

Modular form 285090.2.a.ce

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 5 q^{11} + q^{12} - q^{13} + q^{14} + q^{15} + q^{16} + q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.