Properties

Label 327990.bi
Number of curves $2$
Conductor $327990$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bi1 327990bi1 \([1, 0, 0, -419256, 104243760]\) \(13701674594089/31758480\) \(18890684543512080\) \([2]\) \(4730880\) \(2.0038\) \(\Gamma_0(N)\)-optimal
327990.bi2 327990bi2 \([1, 0, 0, -267876, 180569556]\) \(-3573857582569/21617820900\) \(-12858784020521208900\) \([2]\) \(9461760\) \(2.3504\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 327990.2.a.bi

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.