Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4900.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4900.i1 4900b1 \([0, -1, 0, -24908, 1522312]\) \(-177953104/125\) \(-1200500000000\) \([]\) \(10368\) \(1.2541\) \(\Gamma_0(N)\)-optimal
4900.i2 4900b2 \([0, -1, 0, 24092, 6422312]\) \(161017136/1953125\) \(-18757812500000000\) \([]\) \(31104\) \(1.8034\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4900.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{9} + 6 q^{11} - 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.