Properties

 Label 1110.a Number of curves $4$ Conductor $1110$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

Elliptic curves in class 1110.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.a1 1110c3 $$[1, 1, 0, -358318108, -2610814913072]$$ $$5087799435928552778197163696329/125914832087040$$ $$125914832087040$$ $$[2]$$ $$197120$$ $$3.1512$$
1110.a2 1110c2 $$[1, 1, 0, -22394908, -40800879152]$$ $$1242142983306846366056931529/6179359141291622400$$ $$6179359141291622400$$ $$[2, 2]$$ $$98560$$ $$2.8046$$
1110.a3 1110c4 $$[1, 1, 0, -22016028, -42247518768]$$ $$-1180159344892952613848670409/87759036144023189760000$$ $$-87759036144023189760000$$ $$[2]$$ $$197120$$ $$3.1512$$
1110.a4 1110c1 $$[1, 1, 0, -1423388, -615252528]$$ $$318929057401476905525449/21353131537921474560$$ $$21353131537921474560$$ $$[2]$$ $$49280$$ $$2.4580$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1110.a have rank $$1$$.

Complex multiplication

The elliptic curves in class 1110.a do not have complex multiplication.

Modular form1110.2.a.a

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.