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Properties

Label 327990bn
Number of curves $4$
Conductor $327990$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 327990bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bn3 327990bn1 \([1, 0, 0, -1490690, 700388292]\) \(615882348586441/21715200\) \(12916707380179200\) \([4]\) \(10321920\) \(2.1812\) \(\Gamma_0(N)\)-optimal
327990.bn2 327990bn2 \([1, 0, 0, -1557970, 633686900]\) \(703093388853961/115124490000\) \(68478731470231290000\) \([2, 2]\) \(20643840\) \(2.5278\)  
327990.bn4 327990bn3 \([1, 0, 0, 2832050, 3560074232]\) \(4223169036960119/11647532812500\) \(-6928224148987720312500\) \([2]\) \(41287680\) \(2.8744\)  
327990.bn1 327990bn4 \([1, 0, 0, -7024470, -6561320400]\) \(64443098670429961/6032611833300\) \(3588338204987404389300\) \([2]\) \(41287680\) \(2.8744\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990bn have rank \(1\).

Complex multiplication

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

Modular form 327990.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} + q^{13} - 4 q^{14} + q^{15} + q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.