Properties

Label 74970.ch
Number of curves $2$
Conductor $74970$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 74970.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74970.ch1 74970cy2 \([1, -1, 1, -228668, 31062791]\) \(15417797707369/4080067320\) \(349931547455265720\) \([2]\) \(884736\) \(2.0750\)  
74970.ch2 74970cy1 \([1, -1, 1, 35932, 3121031]\) \(59822347031/83966400\) \(-7201472422334400\) \([2]\) \(442368\) \(1.7284\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 74970.ch have rank \(1\).

Complex multiplication

The elliptic curves in class 74970.ch do not have complex multiplication.

Modular form 74970.2.a.ch

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