# Properties

 Label 310.b Number of curves $2$ Conductor $310$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 310.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310.b1 310a2 $$[1, 1, 1, -1066, -13841]$$ $$133974081659809/192200$$ $$192200$$ $$[2]$$ $$96$$ $$0.28494$$
310.b2 310a1 $$[1, 1, 1, -66, -241]$$ $$-31824875809/1240000$$ $$-1240000$$ $$[2]$$ $$48$$ $$-0.061634$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 310.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 310.b do not have complex multiplication.

## Modular form310.2.a.b

sage: E.q_eigenform(10)

$$q + q^{2} + 2 q^{3} + q^{4} - q^{5} + 2 q^{6} + q^{8} + q^{9} - q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{15} + q^{16} + 2 q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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.