# Properties

 Label 93600bx Number of curves $4$ Conductor $93600$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bx1")

sage: E.isogeny_class()

## Elliptic curves in class 93600bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.h3 93600bx1 $$[0, 0, 0, -19425, 713000]$$ $$1111934656/342225$$ $$249482025000000$$ $$[2, 2]$$ $$294912$$ $$1.4672$$ $$\Gamma_0(N)$$-optimal
93600.h4 93600bx2 $$[0, 0, 0, 53700, 4808000]$$ $$367061696/426465$$ $$-19897151040000000$$ $$$$ $$589824$$ $$1.8138$$
93600.h2 93600bx3 $$[0, 0, 0, -120675, -15588250]$$ $$33324076232/1285245$$ $$7495548840000000$$ $$$$ $$589824$$ $$1.8138$$
93600.h1 93600bx4 $$[0, 0, 0, -282675, 57838250]$$ $$428320044872/73125$$ $$426465000000000$$ $$$$ $$589824$$ $$1.8138$$

## Rank

sage: E.rank()

The elliptic curves in class 93600bx have rank $$1$$.

## Complex multiplication

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

## Modular form 93600.2.a.bx

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 