Properties

 Label 4900.e Number of curves 4 Conductor 4900 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4900.e1")

sage: E.isogeny_class()

Elliptic curves in class 4900.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4900.e1 4900k3 [0, 1, 0, -50633, 4367488] [2] 12960
4900.e2 4900k4 [0, 1, 0, -44508, 5469988] [2] 25920
4900.e3 4900k1 [0, 1, 0, -1633, -18012] [2] 4320 $$\Gamma_0(N)$$-optimal
4900.e4 4900k2 [0, 1, 0, 4492, -116012] [2] 8640

Rank

sage: E.rank()

The elliptic curves in class 4900.e have rank $$1$$.

Modular form4900.2.a.e

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{9} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.