Properties

 Label 4800.cd Number of curves $6$ Conductor $4800$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("cd1")

E.isogeny_class()

Elliptic curves in class 4800.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.cd1 4800r5 $$[0, 1, 0, -320033, -69791937]$$ $$1770025017602/75$$ $$153600000000$$ $$[2]$$ $$24576$$ $$1.6313$$
4800.cd2 4800r3 $$[0, 1, 0, -20033, -1091937]$$ $$868327204/5625$$ $$5760000000000$$ $$[2, 2]$$ $$12288$$ $$1.2847$$
4800.cd3 4800r6 $$[0, 1, 0, -8033, -2375937]$$ $$-27995042/1171875$$ $$-2400000000000000$$ $$[2]$$ $$24576$$ $$1.6313$$
4800.cd4 4800r2 $$[0, 1, 0, -2033, 6063]$$ $$3631696/2025$$ $$518400000000$$ $$[2, 2]$$ $$6144$$ $$0.93814$$
4800.cd5 4800r1 $$[0, 1, 0, -1533, 22563]$$ $$24918016/45$$ $$720000000$$ $$[2]$$ $$3072$$ $$0.59157$$ $$\Gamma_0(N)$$-optimal
4800.cd6 4800r4 $$[0, 1, 0, 7967, 56063]$$ $$54607676/32805$$ $$-33592320000000$$ $$[2]$$ $$12288$$ $$1.2847$$

Rank

sage: E.rank()

The elliptic curves in class 4800.cd have rank $$0$$.

Complex multiplication

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

Modular form4800.2.a.cd

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.