Properties

Label 97461.m
Number of curves $2$
Conductor $97461$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.m1 97461x1 \([1, -1, 1, -26249, 1643240]\) \(23320116793/2873\) \(246406065633\) \([2]\) \(207360\) \(1.2092\) \(\Gamma_0(N)\)-optimal
97461.m2 97461x2 \([1, -1, 1, -24044, 1929008]\) \(-17923019113/8254129\) \(-707924626563609\) \([2]\) \(414720\) \(1.5558\)  

Rank

sage: E.rank()
 

The elliptic curves in class 97461.m have rank \(1\).

Complex multiplication

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

Modular form 97461.2.a.m

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