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Properties

Label 97405e
Number of curves $2$
Conductor $97405$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 97405e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97405.j1 97405e1 \([1, -1, 0, -19685, 1067600]\) \(476196576129/197225\) \(349396118225\) \([2]\) \(201600\) \(1.1769\) \(\Gamma_0(N)\)-optimal
97405.j2 97405e2 \([1, -1, 0, -16660, 1404585]\) \(-288673724529/311181605\) \(-551277195335405\) \([2]\) \(403200\) \(1.5235\)  

Rank

sage: E.rank()
 

The elliptic curves in class 97405e have rank \(0\).

Complex multiplication

The elliptic curves in class 97405e do not have complex multiplication.

Modular form 97405.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} + q^{7} - 3 q^{8} - 3 q^{9} - q^{10} - 4 q^{13} + q^{14} - q^{16} + 6 q^{17} - 3 q^{18} + 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.