Properties

Label 11424r
Number of curves $4$
Conductor $11424$
CM no
Rank $1$
Graph

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

Elliptic curves in class 11424r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11424.s3 11424r1 \([0, 1, 0, -82, -280]\) \(964430272/127449\) \(8156736\) \([2, 2]\) \(1792\) \(0.054141\) \(\Gamma_0(N)\)-optimal
11424.s1 11424r2 \([0, 1, 0, -1272, -17892]\) \(444893916104/9639\) \(4935168\) \([2]\) \(3584\) \(0.40071\)  
11424.s2 11424r3 \([0, 1, 0, -337, 2015]\) \(1036433728/122451\) \(501559296\) \([2]\) \(3584\) \(0.40071\)  
11424.s4 11424r4 \([0, 1, 0, 128, -1288]\) \(449455096/1753941\) \(-898017792\) \([2]\) \(3584\) \(0.40071\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11424r have rank \(1\).

Complex multiplication

The elliptic curves in class 11424r do not have complex multiplication.

Modular form 11424.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} - q^{7} + q^{9} - 2 q^{13} + 2 q^{15} - q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.