Properties

 Label 4950o Number of curves 4 Conductor 4950 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4950.g1")

sage: E.isogeny_class()

Elliptic curves in class 4950o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4950.g3 4950o1 [1, -1, 0, -1242, -15584] [2] 4608 $$\Gamma_0(N)$$-optimal
4950.g4 4950o2 [1, -1, 0, 1008, -67334] [2] 9216
4950.g1 4950o3 [1, -1, 0, -18117, 939541] [2] 13824
4950.g2 4950o4 [1, -1, 0, -9117, 1866541] [2] 27648

Rank

sage: E.rank()

The elliptic curves in class 4950o have rank $$1$$.

Modular form4950.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{7} - q^{8} + q^{11} + 4q^{13} + 2q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

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 Cremona 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 Cremona labels.