Properties

Label 268770r
Number of curves $2$
Conductor $268770$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 268770r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
268770.r2 268770r1 \([1, 0, 1, 646631, 885885692]\) \(1238798620042199/14760960000000\) \(-356293690506240000000\) \([2]\) \(12386304\) \(2.6244\) \(\Gamma_0(N)\)-optimal
268770.r1 268770r2 \([1, 0, 1, -10820889, 12779997436]\) \(5805223604235668521/435937500000000\) \(10522471485937500000000\) \([2]\) \(24772608\) \(2.9710\)  

Rank

sage: E.rank()
 

The elliptic curves in class 268770r have rank \(0\).

Complex multiplication

The elliptic curves in class 268770r do not have complex multiplication.

Modular form 268770.2.a.r

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