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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 129360fl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.du3 | 129360fl1 | \([0, -1, 0, -159560, 24567600]\) | \(932288503609/779625\) | \(375693728256000\) | \([2]\) | \(884736\) | \(1.7246\) | \(\Gamma_0(N)\)-optimal |
| 129360.du2 | 129360fl2 | \([0, -1, 0, -194840, 12939312]\) | \(1697509118089/833765625\) | \(401783570496000000\) | \([2, 2]\) | \(1769472\) | \(2.0711\) | |
| 129360.du4 | 129360fl3 | \([0, -1, 0, 710680, 98420400]\) | \(82375335041831/56396484375\) | \(-27176919000000000000\) | \([2]\) | \(3538944\) | \(2.4177\) | |
| 129360.du1 | 129360fl4 | \([0, -1, 0, -1664840, -817316688]\) | \(1058993490188089/13182390375\) | \(6352466105255424000\) | \([2]\) | \(3538944\) | \(2.4177\) |
Rank
sage: E.rank()
The elliptic curves in class 129360fl have rank \(1\).
Complex multiplication
The elliptic curves in class 129360fl do not have complex multiplication.Modular form 129360.2.a.fl
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 Cremona 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 Cremona labels.
