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Properties

Label 486330cd
Number of curves $2$
Conductor $486330$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 486330cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486330.cd2 486330cd1 \([1, 0, 0, 2098150, 1610422500]\) \(1021488070932591813813599/1711270653287130000000\) \(-1711270653287130000000\) \([7]\) \(29042496\) \(2.7593\) \(\Gamma_0(N)\)-optimal
486330.cd1 486330cd2 \([1, 0, 0, -716997500, -7390008178230]\) \(-40763985302355967860626447640001/1828646593831170189984570\) \(-1828646593831170189984570\) \([]\) \(203297472\) \(3.7323\)  

Rank

sage: E.rank()
 

The elliptic curves in class 486330cd have rank \(1\).

Complex multiplication

The elliptic curves in class 486330cd do not have complex multiplication.

Modular form 486330.2.a.cd

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + q^{13} + q^{14} + q^{15} + q^{16} + 4 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.