Properties

 Label 62400ga Number of curves $2$ Conductor $62400$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ga1")

sage: E.isogeny_class()

Elliptic curves in class 62400ga

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.d2 62400ga1 [0, -1, 0, -516833, 2481537] [2] 1720320 $$\Gamma_0(N)$$-optimal
62400.d1 62400ga2 [0, -1, 0, -5636833, -5132878463] [2] 3440640

Rank

sage: E.rank()

The elliptic curves in class 62400ga have rank $$0$$.

Complex multiplication

The elliptic curves in class 62400ga do not have complex multiplication.

Modular form 62400.2.a.ga

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} - 6q^{11} + q^{13} + 4q^{17} + 2q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.