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Properties

Label 84150.ea
Number of curves $2$
Conductor $84150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ea1")
 
E.isogeny_class()
 

Elliptic curves in class 84150.ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84150.ea1 84150ej2 \([1, -1, 1, -315605, 68319397]\) \(11304275372307/635800\) \(195538303125000\) \([2]\) \(663552\) \(1.8069\)  
84150.ea2 84150ej1 \([1, -1, 1, -18605, 1197397]\) \(-2315685267/658240\) \(-202439655000000\) \([2]\) \(331776\) \(1.4603\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 84150.ea have rank \(1\).

Complex multiplication

The elliptic curves in class 84150.ea do not have complex multiplication.

Modular form 84150.2.a.ea

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{7} + q^{8} + q^{11} - 2 q^{13} - 4 q^{14} + q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) 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.