# Properties

 Label 78400.jd Number of curves $2$ Conductor $78400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("jd1")

sage: E.isogeny_class()

## Elliptic curves in class 78400.jd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.jd1 78400cn2 $$[0, -1, 0, -24033, 1027937]$$ $$2185454/625$$ $$439040000000000$$ $$$$ $$294912$$ $$1.5162$$
78400.jd2 78400cn1 $$[0, -1, 0, 3967, 103937]$$ $$19652/25$$ $$-8780800000000$$ $$$$ $$147456$$ $$1.1696$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 78400.jd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 78400.jd do not have complex multiplication.

## Modular form 78400.2.a.jd

sage: E.q_eigenform(10)

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

## 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. 