Properties

Label 97104cc
Number of curves $2$
Conductor $97104$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 97104cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97104.i2 97104cc1 \([0, -1, 0, 856, 46704]\) \(3442951/49392\) \(-993947222016\) \([2]\) \(184320\) \(0.98277\) \(\Gamma_0(N)\)-optimal
97104.i1 97104cc2 \([0, -1, 0, -15464, 699504]\) \(20324066489/1411788\) \(28410324762624\) \([2]\) \(368640\) \(1.3293\)  

Rank

sage: E.rank()
 

The elliptic curves in class 97104cc have rank \(1\).

Complex multiplication

The elliptic curves in class 97104cc do not have complex multiplication.

Modular form 97104.2.a.cc

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{7} + q^{9} - 6 q^{11} + 6 q^{13} + 2 q^{15} + 6 q^{19} + O(q^{20})\) 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.