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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 152880.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.f1 | 152880ec6 | \([0, -1, 0, -107153216, -426866360640]\) | \(282352188585428161201/20813369346315\) | \(10029760881560016629760\) | \([2]\) | \(18874368\) | \(3.2720\) | |
| 152880.f2 | 152880ec3 | \([0, -1, 0, -36730416, 85693380480]\) | \(11372424889583066401/50586128775\) | \(24376964973567897600\) | \([2]\) | \(9437184\) | \(2.9254\) | |
| 152880.f3 | 152880ec4 | \([0, -1, 0, -7134416, -5747205120]\) | \(83339496416030401/18593645841225\) | \(8960097646896250982400\) | \([2, 2]\) | \(9437184\) | \(2.9254\) | |
| 152880.f4 | 152880ec2 | \([0, -1, 0, -2332416, 1294447680]\) | \(2912015927948401/184878500625\) | \(89091156869245440000\) | \([2, 2]\) | \(4718592\) | \(2.5788\) | |
| 152880.f5 | 152880ec1 | \([0, -1, 0, 117584, 85127680]\) | \(373092501599/6718359375\) | \(-3237512241600000000\) | \([2]\) | \(2359296\) | \(2.2322\) | \(\Gamma_0(N)\)-optimal |
| 152880.f6 | 152880ec5 | \([0, -1, 0, 16052384, -35370660800]\) | \(949279533867428399/1670570708285115\) | \(-805031826469009386024960\) | \([2]\) | \(18874368\) | \(3.2720\) |
Rank
sage: E.rank()
The elliptic curves in class 152880.f have rank \(1\).
Complex multiplication
The elliptic curves in class 152880.f do not have complex multiplication.Modular form 152880.2.a.f
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
