# Properties

 Label 300.b Number of curves $2$ Conductor $300$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 300.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300.b1 300a2 $$[0, -1, 0, -1213, -15863]$$ $$-30866268160/3$$ $$-19200$$ $$[]$$ $$108$$ $$0.25522$$
300.b2 300a1 $$[0, -1, 0, -13, -23]$$ $$-40960/27$$ $$-172800$$ $$[]$$ $$36$$ $$-0.29409$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 300.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 300.b do not have complex multiplication.

## Modular form300.2.a.b

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 