Properties

Label 15680.r
Number of curves $2$
Conductor $15680$
CM no
Rank $0$
Graph

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

Elliptic curves in class 15680.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.r1 15680v2 \([0, 1, 0, -3735041, -2779534241]\) \(544737993463/20000\) \(211569119068160000\) \([2]\) \(430080\) \(2.4121\)  
15680.r2 15680v1 \([0, 1, 0, -222721, -47651745]\) \(-115501303/25600\) \(-270808472407244800\) \([2]\) \(215040\) \(2.0655\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15680.r have rank \(0\).

Complex multiplication

The elliptic curves in class 15680.r do not have complex multiplication.

Modular form 15680.2.a.r

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