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Properties

Label 48074e
Number of curves $3$
Conductor $48074$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 48074e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48074.d3 48074e1 \([1, 1, 1, 886, -16287]\) \(12167/26\) \(-164355439274\) \([]\) \(54180\) \(0.83637\) \(\Gamma_0(N)\)-optimal
48074.d2 48074e2 \([1, 1, 1, -8359, 582789]\) \(-10218313/17576\) \(-111104276949224\) \([]\) \(162540\) \(1.3857\)  
48074.d1 48074e3 \([1, 1, 1, -849654, 301093363]\) \(-10730978619193/6656\) \(-42074992454144\) \([]\) \(487620\) \(1.9350\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48074e have rank \(0\).

Complex multiplication

The elliptic curves in class 48074e do not have complex multiplication.

Modular form 48074.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 3 q^{5} - q^{6} + q^{7} + q^{8} - 2 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} + q^{13} + q^{14} - 3 q^{15} + q^{16} - 3 q^{17} - 2 q^{18} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.