# Properties

 Label 3675.c Number of curves $2$ Conductor $3675$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3675.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.c1 3675n2 $$[0, 1, 1, -22808, 1319294]$$ $$-1713910976512/1594323$$ $$-1220653546875$$ $$[]$$ $$9984$$ $$1.2421$$
3675.c2 3675n1 $$[0, 1, 1, -58, -206]$$ $$-28672/3$$ $$-2296875$$ $$[]$$ $$768$$ $$-0.040369$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3675.c have rank $$1$$.

## Complex multiplication

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

## Modular form3675.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 