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Properties

Label 379050.p
Number of curves $2$
Conductor $379050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 379050.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.p1 379050p1 \([1, 1, 0, -11788500, 14202450000]\) \(1690513270434786979/164670952320000\) \(17648094718170000000000\) \([2]\) \(38707200\) \(3.0059\) \(\Gamma_0(N)\)-optimal
379050.p2 379050p2 \([1, 1, 0, 14279500, 68241414000]\) \(3004566620369762141/20506979587500000\) \(-2197771452979101562500000\) \([2]\) \(77414400\) \(3.3525\)  

Rank

sage: E.rank()
 

The elliptic curves in class 379050.p have rank \(1\).

Complex multiplication

The elliptic curves in class 379050.p do not have complex multiplication.

Modular form 379050.2.a.p

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