Properties

Label 76050v
Number of curves $2$
Conductor $76050$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 76050v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.g2 76050v1 \([1, -1, 0, -29710992, 62341252416]\) \(337135557915/64\) \(550618236675000000\) \([3]\) \(5391360\) \(2.7964\) \(\Gamma_0(N)\)-optimal
76050.g1 76050v2 \([1, -1, 0, -33830367, 43942750541]\) \(682724835/262144\) \(1644137244819763200000000\) \([]\) \(16174080\) \(3.3457\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76050v have rank \(2\).

Complex multiplication

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

Modular form 76050.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 4 q^{7} - q^{8} - 3 q^{11} + 4 q^{14} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.