Properties

 Label 3150.w Number of curves 6 Conductor 3150 CM no Rank 1 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3150.w1")

sage: E.isogeny_class()

Elliptic curves in class 3150.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.w1 3150bi5 [1, -1, 1, -3780005, 2829643247] [2] 49152
3150.w2 3150bi4 [1, -1, 1, -236255, 44255747] [2, 2] 24576
3150.w3 3150bi6 [1, -1, 1, -220505, 50398247] [2] 49152
3150.w4 3150bi3 [1, -1, 1, -83255, -8718253] [2] 24576
3150.w5 3150bi2 [1, -1, 1, -15755, 596747] [2, 2] 12288
3150.w6 3150bi1 [1, -1, 1, 2245, 56747] [4] 6144 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 3150.w have rank $$1$$.

Modular form3150.2.a.w

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.