Properties

Label 334620.be
Number of curves $4$
Conductor $334620$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 334620.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
334620.be1 334620be4 \([0, 0, 0, -2367183, 761493382]\) \(1628514404944/664335375\) \(598432244734168416000\) \([2]\) \(14929920\) \(2.6844\)  
334620.be2 334620be2 \([0, 0, 0, -1089543, -437699522]\) \(158792223184/16335\) \(14714541909999360\) \([2]\) \(4976640\) \(2.1351\)  
334620.be3 334620be1 \([0, 0, 0, -62868, -7933367]\) \(-488095744/200475\) \(-11286722487783600\) \([2]\) \(2488320\) \(1.7885\) \(\Gamma_0(N)\)-optimal
334620.be4 334620be3 \([0, 0, 0, 484692, 86739757]\) \(223673040896/187171875\) \(-10537757878254750000\) \([2]\) \(7464960\) \(2.3378\)  

Rank

sage: E.rank()
 

The elliptic curves in class 334620.be have rank \(1\).

Complex multiplication

The elliptic curves in class 334620.be do not have complex multiplication.

Modular form 334620.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{7} - q^{11} + 6 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.