# Properties

 Label 380.b Number of curves $2$ Conductor $380$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 380.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
380.b1 380b1 $$[0, -1, 0, -921, 10346]$$ $$5405726654464/407253125$$ $$6516050000$$ $$$$ $$240$$ $$0.62837$$ $$\Gamma_0(N)$$-optimal
380.b2 380b2 $$[0, -1, 0, 884, 44280]$$ $$298091207216/3525390625$$ $$-902500000000$$ $$$$ $$480$$ $$0.97495$$

## Rank

sage: E.rank()

The elliptic curves in class 380.b have rank $$0$$.

## Complex multiplication

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

## Modular form380.2.a.b

sage: E.q_eigenform(10)

$$q + 2 q^{3} - q^{5} + 2 q^{7} + q^{9} + 6 q^{13} - 2 q^{15} + 2 q^{17} - q^{19} + O(q^{20})$$

## 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. 