Properties

Label 374850cm
Number of curves $2$
Conductor $374850$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 374850cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374850.cm2 374850cm1 \([1, -1, 0, 898308, 391027216]\) \(59822347031/83966400\) \(-112523006598975000000\) \([2]\) \(10616832\) \(2.5331\) \(\Gamma_0(N)\)-optimal
374850.cm1 374850cm2 \([1, -1, 0, -5716692, 3877132216]\) \(15417797707369/4080067320\) \(5467680428988526875000\) \([2]\) \(21233664\) \(2.8797\)  

Rank

sage: E.rank()
 

The elliptic curves in class 374850cm have rank \(1\).

Complex multiplication

The elliptic curves in class 374850cm do not have complex multiplication.

Modular form 374850.2.a.cm

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