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Properties

Label 386334bm
Number of curves $2$
Conductor $386334$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 386334bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
386334.bm2 386334bm1 \([1, -1, 1, -155059898, -736133011207]\) \(117174888570509216929/1273887851544576\) \(4482484929836171013390336\) \([]\) \(69543936\) \(3.5453\) \(\Gamma_0(N)\)-optimal
386334.bm1 386334bm2 \([1, -1, 1, -34011242258, 2414256301723673]\) \(1236526859255318155975783969/38367061931916216\) \(135003859800830791824728376\) \([]\) \(486807552\) \(4.5183\)  

Rank

sage: E.rank()
 

The elliptic curves in class 386334bm have rank \(0\).

Complex multiplication

The elliptic curves in class 386334bm do not have complex multiplication.

Modular form 386334.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 5 q^{11} - q^{14} + q^{16} + 3 q^{17} + q^{19} + O(q^{20})\) 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.