Properties

Label 185130.fr
Number of curves $4$
Conductor $185130$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fr1")
 
E.isogeny_class()
 

Elliptic curves in class 185130.fr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185130.fr1 185130w4 \([1, -1, 1, -7123172, -7315545729]\) \(30949975477232209/478125000\) \(617483122678125000\) \([2]\) \(7864320\) \(2.5488\)  
185130.fr2 185130w2 \([1, -1, 1, -458492, -107027841]\) \(8253429989329/936360000\) \(1209278947452840000\) \([2, 2]\) \(3932160\) \(2.2022\)  
185130.fr3 185130w1 \([1, -1, 1, -110012, 12291711]\) \(114013572049/15667200\) \(20233686963916800\) \([2]\) \(1966080\) \(1.8556\) \(\Gamma_0(N)\)-optimal
185130.fr4 185130w3 \([1, -1, 1, 630508, -539143041]\) \(21464092074671/109596256200\) \(-141540054404617657800\) \([2]\) \(7864320\) \(2.5488\)  

Rank

sage: E.rank()
 

The elliptic curves in class 185130.fr have rank \(0\).

Complex multiplication

The elliptic curves in class 185130.fr do not have complex multiplication.

Modular form 185130.2.a.fr

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 4 q^{7} + q^{8} + q^{10} + 2 q^{13} + 4 q^{14} + q^{16} + q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.