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Properties

Label 97006.a
Number of curves $2$
Conductor $97006$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 97006.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97006.a1 97006e2 \([1, -1, 0, -1624311844, -25196790850568]\) \(98191033604529537629349729/10906239337336\) \(52642334189607440824\) \([]\) \(58084992\) \(3.6532\)  
97006.a2 97006e1 \([1, -1, 0, -3270604, 2096481232]\) \(801581275315909089/70810888830976\) \(341790635507354435584\) \([]\) \(8297856\) \(2.6803\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 97006.a have rank \(0\).

Complex multiplication

The elliptic curves in class 97006.a do not have complex multiplication.

Modular form 97006.2.a.a

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.