Properties

 Label 49419.j Number of curves $3$ Conductor $49419$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

Elliptic curves in class 49419.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49419.j1 49419f3 $$[0, 0, 1, -2001036, 1089508108]$$ $$-50357871050752/19$$ $$-334329468219$$ $$[]$$ $$362880$$ $$1.9994$$
49419.j2 49419f2 $$[0, 0, 1, -24276, 1548823]$$ $$-89915392/6859$$ $$-120692938027059$$ $$[]$$ $$120960$$ $$1.4500$$
49419.j3 49419f1 $$[0, 0, 1, 1734, 1228]$$ $$32768/19$$ $$-334329468219$$ $$[]$$ $$40320$$ $$0.90074$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 49419.j have rank $$1$$.

Complex multiplication

The elliptic curves in class 49419.j do not have complex multiplication.

Modular form 49419.2.a.j

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{5} + q^{7} + 3q^{11} - 4q^{13} + 4q^{16} + q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.