Properties

Label 327990.r
Number of curves $6$
Conductor $327990$
CM no
Rank $0$
Graph

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

Elliptic curves in class 327990.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.r1 327990r6 \([1, 0, 1, -7581633, -8035747934]\) \(81025909800741361/11088090\) \(6595454517346890\) \([2]\) \(12386304\) \(2.4477\)  
327990.r2 327990r3 \([1, 0, 1, -710663, 230350238]\) \(66730743078481/60937500\) \(36247046123437500\) \([2]\) \(6193152\) \(2.1011\)  
327990.r3 327990r4 \([1, 0, 1, -475183, -124847794]\) \(19948814692561/231344100\) \(137608865855756100\) \([2, 2]\) \(6193152\) \(2.1011\)  
327990.r4 327990r5 \([1, 0, 1, -96733, -318160054]\) \(-168288035761/73415764890\) \(-43669409085624999690\) \([2]\) \(12386304\) \(2.4477\)  
327990.r5 327990r2 \([1, 0, 1, -54683, 1806806]\) \(30400540561/15210000\) \(9047262712410000\) \([2, 2]\) \(3096576\) \(1.7546\)  
327990.r6 327990r1 \([1, 0, 1, 12597, 218998]\) \(371694959/249600\) \(-148467900921600\) \([2]\) \(1548288\) \(1.4080\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 327990.r have rank \(0\).

Complex multiplication

The elliptic curves in class 327990.r do not have complex multiplication.

Modular form 327990.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} + q^{13} + q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.