Properties

Label 158400bh
Number of curves $2$
Conductor $158400$
CM no
Rank $1$
Graph

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

Elliptic curves in class 158400bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.jx1 158400bh1 \([0, 0, 0, -21000, 1228750]\) \(-56197120/3267\) \(-59541075000000\) \([]\) \(414720\) \(1.3994\) \(\Gamma_0(N)\)-optimal
158400.jx2 158400bh2 \([0, 0, 0, 114000, 2173750]\) \(8990228480/5314683\) \(-96860097675000000\) \([]\) \(1244160\) \(1.9487\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158400bh have rank \(1\).

Complex multiplication

The elliptic curves in class 158400bh do not have complex multiplication.

Modular form 158400.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{7} + q^{11} + q^{13} + 6 q^{17} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.