# Properties

 Label 93600.bg Number of curves $2$ Conductor $93600$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 93600.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.bg1 93600f2 $$[0, 0, 0, -78300, 7668000]$$ $$42144192/4225$$ $$5322283200000000$$ $$$$ $$442368$$ $$1.7538$$
93600.bg2 93600f1 $$[0, 0, 0, 6075, 580500]$$ $$1259712/8125$$ $$-159924375000000$$ $$$$ $$221184$$ $$1.4073$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 93600.bg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 93600.bg do not have complex multiplication.

## Modular form 93600.2.a.bg

sage: E.q_eigenform(10)

$$q - 2q^{7} - 4q^{11} + q^{13} - 4q^{17} + 2q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 