# Properties

 Label 2300.d Number of curves $2$ Conductor $2300$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 2300.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2300.d1 2300a1 $$[0, -1, 0, -1158, 68437]$$ $$-687518464/7604375$$ $$-1901093750000$$ $$[]$$ $$3456$$ $$1.0381$$ $$\Gamma_0(N)$$-optimal
2300.d2 2300a2 $$[0, -1, 0, 10342, -1760063]$$ $$489277573376/5615234375$$ $$-1403808593750000$$ $$[]$$ $$10368$$ $$1.5874$$

## Rank

sage: E.rank()

The elliptic curves in class 2300.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2300.d do not have complex multiplication.

## Modular form2300.2.a.d

sage: E.q_eigenform(10)

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