# Properties

 Label 378.g Number of curves $3$ Conductor $378$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 378.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
378.g1 378e2 $$[1, -1, 1, -1271, -17117]$$ $$-11527859979/28$$ $$-551124$$ $$[]$$ $$216$$ $$0.34195$$
378.g2 378e1 $$[1, -1, 1, -11, -37]$$ $$-5000211/21952$$ $$-592704$$ $$$$ $$72$$ $$-0.20736$$ $$\Gamma_0(N)$$-optimal
378.g3 378e3 $$[1, -1, 1, 94, 929]$$ $$381790581/1835008$$ $$-445906944$$ $$$$ $$216$$ $$0.34195$$

## Rank

sage: E.rank()

The elliptic curves in class 378.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 378.g do not have complex multiplication.

## Modular form378.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 3 q^{5} + q^{7} + q^{8} + 3 q^{10} - 3 q^{11} - 4 q^{13} + q^{14} + q^{16} + 6 q^{17} - 7 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 