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Properties

Label 245490bh
Number of curves $2$
Conductor $245490$
CM no
Rank $0$
Graph

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

Elliptic curves in class 245490bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
245490.bh2 245490bh1 \([1, 1, 1, -72521, -32451721]\) \(-358531401121921/3652290000000\) \(-429688266210000000\) \([]\) \(3556224\) \(2.0657\) \(\Gamma_0(N)\)-optimal
245490.bh1 245490bh2 \([1, 1, 1, -18645971, 31456409459]\) \(-6093832136609347161121/108676727597808690\) \(-12785708325154594569810\) \([]\) \(24893568\) \(3.0386\)  

Rank

sage: E.rank()
 

The elliptic curves in class 245490bh have rank \(0\).

Complex multiplication

The elliptic curves in class 245490bh do not have complex multiplication.

Modular form 245490.2.a.bh

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.