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Properties

Label 303450.ey
Number of curves $2$
Conductor $303450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ey1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.ey1 303450ey2 \([1, 1, 1, -3746313, 2054516031]\) \(15417797707369/4080067320\) \(1538795413455391875000\) \([2]\) \(15925248\) \(2.7740\)  
303450.ey2 303450ey1 \([1, 1, 1, 588687, 207806031]\) \(59822347031/83966400\) \(-31667887088775000000\) \([2]\) \(7962624\) \(2.4274\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 303450.ey have rank \(1\).

Complex multiplication

The elliptic curves in class 303450.ey do not have complex multiplication.

Modular form 303450.2.a.ey

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