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Properties

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

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 96330.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.ba1 96330bf4 \([1, 0, 1, -513764, 141697376]\) \(3107086841064961/570\) \(2751281130\) \([2]\) \(884736\) \(1.6470\)  
96330.ba2 96330bf3 \([1, 0, 1, -37184, 1465232]\) \(1177918188481/488703750\) \(2358879658833750\) \([2]\) \(884736\) \(1.6470\)  
96330.ba3 96330bf2 \([1, 0, 1, -32114, 2211536]\) \(758800078561/324900\) \(1568230244100\) \([2, 2]\) \(442368\) \(1.3004\)  
96330.ba4 96330bf1 \([1, 0, 1, -1694, 45632]\) \(-111284641/123120\) \(-594276724080\) \([2]\) \(221184\) \(0.95384\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 96330.2.a.ba

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.