Properties

Label 344760br
Number of curves $6$
Conductor $344760$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 344760br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.br4 344760br1 \([0, 1, 0, -2801231, 1803627294]\) \(31476797652269056/49725\) \(3840209240400\) \([2]\) \(3784704\) \(2.1091\) \(\Gamma_0(N)\)-optimal
344760.br3 344760br2 \([0, 1, 0, -2802076, 1802483840]\) \(1969080716416336/2472575625\) \(3055270471662240000\) \([2, 2]\) \(7569408\) \(2.4557\)  
344760.br5 344760br3 \([0, 1, 0, -2055096, 2786107104]\) \(-194204905090564/566398828125\) \(-2799512536251600000000\) \([2]\) \(15138816\) \(2.8023\)  
344760.br2 344760br4 \([0, 1, 0, -3562576, 745693040]\) \(1011710313226084/536724738225\) \(2652843824114763801600\) \([2, 2]\) \(15138816\) \(2.8023\)  
344760.br6 344760br5 \([0, 1, 0, 13574024, 5845545200]\) \(27980756504588158/17683545112935\) \(-174807233951786341201920\) \([2]\) \(30277632\) \(3.1488\)  
344760.br1 344760br6 \([0, 1, 0, -32867176, -71976602320]\) \(397210600760070242/3536192675535\) \(34956342542349143685120\) \([2]\) \(30277632\) \(3.1488\)  

Rank

sage: E.rank()
 

The elliptic curves in class 344760br have rank \(1\).

Complex multiplication

The elliptic curves in class 344760br do not have complex multiplication.

Modular form 344760.2.a.br

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.