# Properties

 Label 1960.g Number of curves 4 Conductor 1960 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1960.g1")

sage: E.isogeny_class()

## Elliptic curves in class 1960.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1960.g1 1960b3 [0, 0, 0, -5243, 146118]  1152
1960.g2 1960b2 [0, 0, 0, -343, 2058] [2, 2] 576
1960.g3 1960b1 [0, 0, 0, -98, -343]  288 $$\Gamma_0(N)$$-optimal
1960.g4 1960b4 [0, 0, 0, 637, 11662]  1152

## Rank

sage: E.rank()

The elliptic curves in class 1960.g have rank $$0$$.

## Modular form1960.2.a.g

sage: E.q_eigenform(10)

$$q - q^{5} - 3q^{9} + 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 