# Properties

 Label 3675.l Number of curves $2$ Conductor $3675$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 3675.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.l1 3675p1 $$[1, 0, 1, -22076, -1223827]$$ $$5177717/189$$ $$43429025390625$$ $$[2]$$ $$11520$$ $$1.3865$$ $$\Gamma_0(N)$$-optimal
3675.l2 3675p2 $$[1, 0, 1, 8549, -4347577]$$ $$300763/35721$$ $$-8208085798828125$$ $$[2]$$ $$23040$$ $$1.7330$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3675.2.a.l

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.