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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 48552.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48552.f1 | 48552i4 | \([0, -1, 0, -44024, 3565500]\) | \(381775972/567\) | \(14014465661952\) | \([2]\) | \(147456\) | \(1.4236\) | |
| 48552.f2 | 48552i2 | \([0, -1, 0, -3564, 21204]\) | \(810448/441\) | \(2725034989824\) | \([2, 2]\) | \(73728\) | \(1.0770\) | |
| 48552.f3 | 48552i1 | \([0, -1, 0, -2119, -36596]\) | \(2725888/21\) | \(8110223184\) | \([2]\) | \(36864\) | \(0.73042\) | \(\Gamma_0(N)\)-optimal |
| 48552.f4 | 48552i3 | \([0, -1, 0, 13776, 152988]\) | \(11696828/7203\) | \(-178035619335168\) | \([2]\) | \(147456\) | \(1.4236\) |
Rank
sage: E.rank()
The elliptic curves in class 48552.f have rank \(0\).
Complex multiplication
The elliptic curves in class 48552.f do not have complex multiplication.Modular form 48552.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
