# Properties

 Label 441.c Number of curves $4$ Conductor $441$ CM $$\Q(\sqrt{-7})$$ Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 441.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
441.c1 441d4 $$[1, -1, 1, -16400, -804212]$$ $$16581375$$ $$29417779503$$ $$[2]$$ $$448$$ $$1.0697$$   $$-28$$
441.c2 441d3 $$[1, -1, 1, -965, -13940]$$ $$-3375$$ $$-29417779503$$ $$[2]$$ $$224$$ $$0.72312$$   $$-7$$
441.c3 441d2 $$[1, -1, 1, -335, 2440]$$ $$16581375$$ $$250047$$ $$[2]$$ $$64$$ $$0.096741$$   $$-28$$
441.c4 441d1 $$[1, -1, 1, -20, 46]$$ $$-3375$$ $$-250047$$ $$[2]$$ $$32$$ $$-0.24983$$ $$\Gamma_0(N)$$-optimal $$-7$$

## Rank

sage: E.rank()

The elliptic curves in class 441.c have rank $$1$$.

## Complex multiplication

Each elliptic curve in class 441.c has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-7})$$.

## Modular form441.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 3 q^{8} - 4 q^{11} - q^{16} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.