Properties

 Label 4410.bc Number of curves $4$ Conductor $4410$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

Elliptic curves in class 4410.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.bc1 4410be3 [1, -1, 1, -164723, 25773437] [2] 24576
4410.bc2 4410be2 [1, -1, 1, -10373, 398297] [2, 2] 12288
4410.bc3 4410be1 [1, -1, 1, -1553, -14479] [2] 6144 $$\Gamma_0(N)$$-optimal
4410.bc4 4410be4 [1, -1, 1, 2857, 1334981] [2] 24576

Rank

sage: E.rank()

The elliptic curves in class 4410.bc have rank $$0$$.

Complex multiplication

The elliptic curves in class 4410.bc do not have complex multiplication.

Modular form4410.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 4q^{11} + 2q^{13} + q^{16} - 6q^{17} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.