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Properties

Label 407330p
Number of curves $2$
Conductor $407330$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 407330p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
407330.p2 407330p1 \([1, 1, 0, -12672, -495616]\) \(18498190416623/2168320000\) \(26381949440000\) \([2]\) \(1216512\) \(1.3068\) \(\Gamma_0(N)\)-optimal
407330.p1 407330p2 \([1, 1, 0, -196672, -33652416]\) \(69146667954384623/1147854400\) \(13965944484800\) \([2]\) \(2433024\) \(1.6534\)  

Rank

sage: E.rank()
 

The elliptic curves in class 407330p have rank \(0\).

Complex multiplication

The elliptic curves in class 407330p do not have complex multiplication.

Modular form 407330.2.a.p

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.