Properties

Label 76050.ev
Number of curves $4$
Conductor $76050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ev1")
 
E.isogeny_class()
 

Elliptic curves in class 76050.ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.ev1 76050ec4 \([1, -1, 1, -18385880, 30343338497]\) \(12501706118329/2570490\) \(141326494534576406250\) \([2]\) \(4128768\) \(2.8635\)  
76050.ev2 76050ec2 \([1, -1, 1, -1274630, 364428497]\) \(4165509529/1368900\) \(75262630225514062500\) \([2, 2]\) \(2064384\) \(2.5170\)  
76050.ev3 76050ec1 \([1, -1, 1, -514130, -137501503]\) \(273359449/9360\) \(514616275046250000\) \([2]\) \(1032192\) \(2.1704\) \(\Gamma_0(N)\)-optimal
76050.ev4 76050ec3 \([1, -1, 1, 3668620, 2499912497]\) \(99317171591/106616250\) \(-5861801007948691406250\) \([2]\) \(4128768\) \(2.8635\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76050.ev have rank \(1\).

Complex multiplication

The elliptic curves in class 76050.ev do not have complex multiplication.

Modular form 76050.2.a.ev

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} + q^{16} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.