# Properties

 Label 4800.bz Number of curves $8$ Conductor $4800$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("bz1")

E.isogeny_class()

## Elliptic curves in class 4800.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.bz1 4800cd7 $$[0, 1, 0, -3456033, 2471796063]$$ $$1114544804970241/405$$ $$1658880000000$$ $$[2]$$ $$49152$$ $$2.1353$$
4800.bz2 4800cd5 $$[0, 1, 0, -216033, 38556063]$$ $$272223782641/164025$$ $$671846400000000$$ $$[2, 2]$$ $$24576$$ $$1.7887$$
4800.bz3 4800cd8 $$[0, 1, 0, -176033, 53316063]$$ $$-147281603041/215233605$$ $$-881596846080000000$$ $$[2]$$ $$49152$$ $$2.1353$$
4800.bz4 4800cd3 $$[0, 1, 0, -128033, -17675937]$$ $$56667352321/15$$ $$61440000000$$ $$[2]$$ $$12288$$ $$1.4422$$
4800.bz5 4800cd4 $$[0, 1, 0, -16033, 356063]$$ $$111284641/50625$$ $$207360000000000$$ $$[2, 2]$$ $$12288$$ $$1.4422$$
4800.bz6 4800cd2 $$[0, 1, 0, -8033, -275937]$$ $$13997521/225$$ $$921600000000$$ $$[2, 2]$$ $$6144$$ $$1.0956$$
4800.bz7 4800cd1 $$[0, 1, 0, -33, -11937]$$ $$-1/15$$ $$-61440000000$$ $$[2]$$ $$3072$$ $$0.74901$$ $$\Gamma_0(N)$$-optimal
4800.bz8 4800cd6 $$[0, 1, 0, 55967, 2732063]$$ $$4733169839/3515625$$ $$-14400000000000000$$ $$[2]$$ $$24576$$ $$1.7887$$

## Rank

sage: E.rank()

The elliptic curves in class 4800.bz have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4800.bz do not have complex multiplication.

## Modular form4800.2.a.bz

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.