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SageMath
E = EllipticCurve("lb1")
E.isogeny_class()
Elliptic curves in class 369600.lb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.lb1 | 369600lb3 | \([0, -1, 0, -52785633, 147627799137]\) | \(3971101377248209009/56495958750\) | \(231407447040000000000\) | \([2]\) | \(28311552\) | \(3.0472\) | |
| 369600.lb2 | 369600lb2 | \([0, -1, 0, -3393633, 2168359137]\) | \(1055257664218129/115307784900\) | \(472300686950400000000\) | \([2, 2]\) | \(14155776\) | \(2.7006\) | |
| 369600.lb3 | 369600lb1 | \([0, -1, 0, -801633, -239608863]\) | \(13908844989649/1980372240\) | \(8111604695040000000\) | \([2]\) | \(7077888\) | \(2.3541\) | \(\Gamma_0(N)\)-optimal |
| 369600.lb4 | 369600lb4 | \([0, -1, 0, 4526367, 10777399137]\) | \(2503876820718671/13702874328990\) | \(-56126973251543040000000\) | \([2]\) | \(28311552\) | \(3.0472\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.lb have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.lb do not have complex multiplication.Modular form 369600.2.a.lb
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.
