# Properties

 Label 1224.d Number of curves $2$ Conductor $1224$ CM no Rank $1$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 1224.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1224.d1 1224d2 $$[0, 0, 0, -435, -3346]$$ $$6097250/289$$ $$431474688$$ $$$$ $$384$$ $$0.41746$$
1224.d2 1224d1 $$[0, 0, 0, -75, 182]$$ $$62500/17$$ $$12690432$$ $$$$ $$192$$ $$0.070888$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1224.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1224.d do not have complex multiplication.

## Modular form1224.2.a.d

sage: E.q_eigenform(10)

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

## 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. 