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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 47190.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47190.w1 | 47190y4 | \([1, 0, 1, -144719, 20099792]\) | \(189208196468929/10860320250\) | \(19239719802410250\) | \([2]\) | \(414720\) | \(1.8788\) | |
| 47190.w2 | 47190y2 | \([1, 0, 1, -24929, -1510324]\) | \(967068262369/4928040\) | \(8730323470440\) | \([2]\) | \(138240\) | \(1.3295\) | |
| 47190.w3 | 47190y1 | \([1, 0, 1, -729, -48644]\) | \(-24137569/561600\) | \(-994908657600\) | \([2]\) | \(69120\) | \(0.98289\) | \(\Gamma_0(N)\)-optimal |
| 47190.w4 | 47190y3 | \([1, 0, 1, 6531, 1284292]\) | \(17394111071/411937500\) | \(-729772409437500\) | \([2]\) | \(207360\) | \(1.5322\) |
Rank
sage: E.rank()
The elliptic curves in class 47190.w have rank \(1\).
Complex multiplication
The elliptic curves in class 47190.w do not have complex multiplication.Modular form 47190.2.a.w
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
