Properties

Label 352800bi
Number of curves $2$
Conductor $352800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 352800bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.bi2 352800bi1 \([0, 0, 0, -76125, -7962500]\) \(1560896/27\) \(843908625000000\) \([2]\) \(1720320\) \(1.6611\) \(\Gamma_0(N)\)-optimal
352800.bi1 352800bi2 \([0, 0, 0, -154875, 11331250]\) \(1643032/729\) \(182284263000000000\) \([2]\) \(3440640\) \(2.0077\)  

Rank

sage: E.rank()
 

The elliptic curves in class 352800bi have rank \(0\).

Complex multiplication

The elliptic curves in class 352800bi do not have complex multiplication.

Modular form 352800.2.a.bi

sage: E.q_eigenform(10)
 
\(q - 4 q^{11} - 6 q^{13} - 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.