# Properties

 Label 380.a Number of curves $2$ Conductor $380$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 380.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
380.a1 380a2 $$[0, 0, 0, -103, -402]$$ $$472058064/475$$ $$121600$$ $$$$ $$48$$ $$-0.10516$$
380.a2 380a1 $$[0, 0, 0, -8, -3]$$ $$3538944/1805$$ $$28880$$ $$$$ $$24$$ $$-0.45173$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 380.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 380.a do not have complex multiplication.

## Modular form380.2.a.a

sage: E.q_eigenform(10)

$$q - q^{5} - 2 q^{7} - 3 q^{9} - 4 q^{11} - 4 q^{13} + 6 q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 