↑

Properties

Label 308898.bh
Number of curves $2$
Conductor $308898$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 308898.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308898.bh1 308898bh2 \([1, -1, 1, -35066876423, -2527502696594467]\) \(1294373635812597347281/2083292441154\) \(7675479928710770729718259746\) \([]\) \(576576000\) \(4.6150\)  
308898.bh2 308898bh1 \([1, -1, 1, -329751833, 2190745461593]\) \(1076291879750641/60150618144\) \(221613083762775241348724256\) \([]\) \(115315200\) \(3.8103\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308898.bh have rank \(0\).

Complex multiplication

The elliptic curves in class 308898.bh do not have complex multiplication.

Modular form 308898.2.a.bh

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.