Properties

Label 46800bh
Number of curves $2$
Conductor $46800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 46800bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.h1 46800bh1 \([0, 0, 0, -750, -3625]\) \(256000/117\) \(21323250000\) \([2]\) \(36864\) \(0.67685\) \(\Gamma_0(N)\)-optimal
46800.h2 46800bh2 \([0, 0, 0, 2625, -27250]\) \(686000/507\) \(-1478412000000\) \([2]\) \(73728\) \(1.0234\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46800bh have rank \(1\).

Complex multiplication

The elliptic curves in class 46800bh do not have complex multiplication.

Modular form 46800.2.a.bh

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 2q^{11} + q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 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.