Properties

Label 4900p
Number of curves $2$
Conductor $4900$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 4900p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4900.m1 4900p1 \([0, 0, 0, -98000, 11790625]\) \(28311552/49\) \(180150031250000\) \([2]\) \(17280\) \(1.6293\) \(\Gamma_0(N)\)-optimal
4900.m2 4900p2 \([0, 0, 0, -67375, 19293750]\) \(-574992/2401\) \(-141237624500000000\) \([2]\) \(34560\) \(1.9759\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4900p have rank \(0\).

Complex multiplication

The elliptic curves in class 4900p do not have complex multiplication.

Modular form 4900.2.a.p

sage: E.q_eigenform(10)
 
\(q - 3 q^{9} + 4 q^{13} + 4 q^{17} - 4 q^{19} + O(q^{20})\) 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.