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Properties

Label 96330.l
Number of curves $2$
Conductor $96330$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 96330.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.l1 96330b2 \([1, 1, 0, -5073, -139017]\) \(2992209121/54150\) \(261371707350\) \([2]\) \(184320\) \(0.98605\)  
96330.l2 96330b1 \([1, 1, 0, -3, -6183]\) \(-1/3420\) \(-16507686780\) \([2]\) \(92160\) \(0.63947\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 96330.2.a.l

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