Properties

Label 97461.l
Number of curves $2$
Conductor $97461$
CM no
Rank $0$
Graph

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

Elliptic curves in class 97461.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.l1 97461d2 \([1, -1, 1, -26984, 658928]\) \(684030715731/338005577\) \(1073682489468771\) \([2]\) \(368640\) \(1.5772\)  
97461.l2 97461d1 \([1, -1, 1, -14489, -660544]\) \(105890949891/1288651\) \(4093429540473\) \([2]\) \(184320\) \(1.2307\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 97461.l have rank \(0\).

Complex multiplication

The elliptic curves in class 97461.l do not have complex multiplication.

Modular form 97461.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 2q^{5} + 3q^{8} - 2q^{10} + q^{13} - q^{16} + q^{17} + 8q^{19} + O(q^{20})\)  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 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.