Properties

 Label 405600bg Number of curves $2$ Conductor $405600$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

Elliptic curves in class 405600bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.bg1 405600bg1 $$[0, -1, 0, -44744158, 115005365812]$$ $$2052450196928704/4317958125$$ $$20841959139373125000000$$ $$[2]$$ $$37158912$$ $$3.1677$$ $$\Gamma_0(N)$$-optimal
405600.bg2 405600bg2 $$[0, -1, 0, -29344033, 195347817937]$$ $$-9045718037056/48125390625$$ $$-14866692390225000000000000$$ $$[2]$$ $$74317824$$ $$3.5143$$

Rank

sage: E.rank()

The elliptic curves in class 405600bg have rank $$1$$.

Complex multiplication

The elliptic curves in class 405600bg do not have complex multiplication.

Modular form 405600.2.a.bg

sage: E.q_eigenform(10)

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

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.