Properties

Label 96330u
Number of curves $4$
Conductor $96330$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 96330u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.r3 96330u1 \([1, 1, 0, -5242, 143044]\) \(3301293169/22800\) \(110051245200\) \([2]\) \(147456\) \(0.95224\) \(\Gamma_0(N)\)-optimal
96330.r2 96330u2 \([1, 1, 0, -8622, -68544]\) \(14688124849/8122500\) \(39205756102500\) \([2, 2]\) \(294912\) \(1.2988\)  
96330.r4 96330u3 \([1, 1, 0, 33628, -499494]\) \(871257511151/527800050\) \(-2547590031540450\) \([2]\) \(589824\) \(1.6454\)  
96330.r1 96330u4 \([1, 1, 0, -104952, -13111626]\) \(26487576322129/44531250\) \(214943838281250\) \([2]\) \(589824\) \(1.6454\)  

Rank

sage: E.rank()
 

The elliptic curves in class 96330u have rank \(1\).

Complex multiplication

The elliptic curves in class 96330u do not have complex multiplication.

Modular form 96330.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.