Properties

 Label 5610.be Number of curves $4$ Conductor $5610$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("be1")

E.isogeny_class()

Elliptic curves in class 5610.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.be1 5610be4 $$[1, 0, 0, -178426, -25264420]$$ $$628200507126935410849/88124751829125000$$ $$88124751829125000$$ $$[2]$$ $$82944$$ $$1.9777$$
5610.be2 5610be2 $$[1, 0, 0, -45586, 3738116]$$ $$10476561483361670689/13992628953600$$ $$13992628953600$$ $$[6]$$ $$27648$$ $$1.4283$$
5610.be3 5610be1 $$[1, 0, 0, -2066, 91140]$$ $$-975276594443809/3037581803520$$ $$-3037581803520$$ $$[6]$$ $$13824$$ $$1.0818$$ $$\Gamma_0(N)$$-optimal
5610.be4 5610be3 $$[1, 0, 0, 18094, -2114364]$$ $$655127711084516831/2313151512408000$$ $$-2313151512408000$$ $$[2]$$ $$41472$$ $$1.6311$$

Rank

sage: E.rank()

The elliptic curves in class 5610.be have rank $$1$$.

Complex multiplication

The elliptic curves in class 5610.be do not have complex multiplication.

Modular form5610.2.a.be

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + 2 q^{13} - 4 q^{14} - q^{15} + q^{16} - q^{17} + q^{18} + 2 q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.