# Properties

 Label 3675.q Number of curves $2$ Conductor $3675$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 3675.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.q1 3675q1 $$[0, 1, 1, -408, 3119]$$ $$-102400/3$$ $$-220591875$$ $$[]$$ $$1980$$ $$0.37986$$ $$\Gamma_0(N)$$-optimal
3675.q2 3675q2 $$[0, 1, 1, 2042, -156131]$$ $$20480/243$$ $$-11167463671875$$ $$[]$$ $$9900$$ $$1.1846$$

## Rank

sage: E.rank()

The elliptic curves in class 3675.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3675.q do not have complex multiplication.

## Modular form3675.2.a.q

sage: E.q_eigenform(10)

$$q + 2q^{2} + q^{3} + 2q^{4} + 2q^{6} + q^{9} + 2q^{11} + 2q^{12} - q^{13} - 4q^{16} - 2q^{17} + 2q^{18} + 5q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 