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Properties

Label 301665.p
Number of curves $2$
Conductor $301665$
CM no
Rank $0$
Graph

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

Elliptic curves in class 301665.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301665.p1 301665p2 \([1, 0, 0, -211408441, -1047901026550]\) \(216486375407331255135001/27004994294227023375\) \(130347949504323644469660375\) \([2]\) \(87091200\) \(3.7407\)  
301665.p2 301665p1 \([1, 0, 0, 19593434, -84761808925]\) \(172343644217341694999/742780064187984375\) \(-3585257498843140673109375\) \([2]\) \(43545600\) \(3.3941\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301665.p have rank \(0\).

Complex multiplication

The elliptic curves in class 301665.p do not have complex multiplication.

Modular form 301665.2.a.p

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