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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 3150.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.w1 | 3150bi5 | \([1, -1, 1, -3780005, 2829643247]\) | \(524388516989299201/3150\) | \(35880468750\) | \([2]\) | \(49152\) | \(2.0908\) | |
| 3150.w2 | 3150bi4 | \([1, -1, 1, -236255, 44255747]\) | \(128031684631201/9922500\) | \(113023476562500\) | \([2, 2]\) | \(24576\) | \(1.7442\) | |
| 3150.w3 | 3150bi6 | \([1, -1, 1, -220505, 50398247]\) | \(-104094944089921/35880468750\) | \(-408700964355468750\) | \([2]\) | \(49152\) | \(2.0908\) | |
| 3150.w4 | 3150bi3 | \([1, -1, 1, -83255, -8718253]\) | \(5602762882081/345888060\) | \(3939881183437500\) | \([2]\) | \(24576\) | \(1.7442\) | |
| 3150.w5 | 3150bi2 | \([1, -1, 1, -15755, 596747]\) | \(37966934881/8643600\) | \(98456006250000\) | \([2, 2]\) | \(12288\) | \(1.3976\) | |
| 3150.w6 | 3150bi1 | \([1, -1, 1, 2245, 56747]\) | \(109902239/188160\) | \(-2143260000000\) | \([4]\) | \(6144\) | \(1.0511\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.w have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.w do not have complex multiplication.Modular form 3150.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
