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SageMath
E = EllipticCurve("la1")
E.isogeny_class()
Elliptic curves in class 221760la
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.dz3 | 221760la1 | \([0, 0, 0, -141802428, -649929725552]\) | \(26401417552259125806544/507547744790625\) | \(6062117780723558400000\) | \([2]\) | \(31457280\) | \(3.3027\) | \(\Gamma_0(N)\)-optimal |
| 221760.dz2 | 221760la2 | \([0, 0, 0, -146526348, -604309885328]\) | \(7282213870869695463556/912102595400390625\) | \(43576380099584640000000000\) | \([2, 2]\) | \(62914560\) | \(3.6492\) | |
| 221760.dz1 | 221760la3 | \([0, 0, 0, -586609068, 4843386089008]\) | \(233632133015204766393938/29145526885986328125\) | \(2784898462500000000000000000\) | \([2]\) | \(125829120\) | \(3.9958\) | |
| 221760.dz4 | 221760la4 | \([0, 0, 0, 217973652, -3132336085328]\) | \(11986661998777424518222/51295853620928503125\) | \(-4901395141709906415206400000\) | \([2]\) | \(125829120\) | \(3.9958\) |
Rank
sage: E.rank()
The elliptic curves in class 221760la have rank \(1\).
Complex multiplication
The elliptic curves in class 221760la do not have complex multiplication.Modular form 221760.2.a.la
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.
