Properties

 Label 3380.c Number of curves $4$ Conductor $3380$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

Elliptic curves in class 3380.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.c1 3380i3 $$[0, 1, 0, -6985, -226992]$$ $$488095744/125$$ $$9653618000$$ $$[2]$$ $$3456$$ $$0.90183$$
3380.c2 3380i4 $$[0, 1, 0, -6140, -283100]$$ $$-20720464/15625$$ $$-19307236000000$$ $$[2]$$ $$6912$$ $$1.2484$$
3380.c3 3380i1 $$[0, 1, 0, -225, 820]$$ $$16384/5$$ $$386144720$$ $$[2]$$ $$1152$$ $$0.35252$$ $$\Gamma_0(N)$$-optimal
3380.c4 3380i2 $$[0, 1, 0, 620, 6228]$$ $$21296/25$$ $$-30891577600$$ $$[2]$$ $$2304$$ $$0.69910$$

Rank

sage: E.rank()

The elliptic curves in class 3380.c have rank $$1$$.

Complex multiplication

The elliptic curves in class 3380.c do not have complex multiplication.

Modular form3380.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} - 2q^{7} + q^{9} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.