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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 65520.ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.ee1 | 65520bm4 | \([0, 0, 0, -224787, -41020814]\) | \(841356017734178/1404585\) | \(2097034168320\) | \([2]\) | \(327680\) | \(1.6265\) | |
| 65520.ee2 | 65520bm3 | \([0, 0, 0, -36867, 1880674]\) | \(3711757787138/1124589375\) | \(1679002940160000\) | \([2]\) | \(327680\) | \(1.6265\) | |
| 65520.ee3 | 65520bm2 | \([0, 0, 0, -14187, -627734]\) | \(423026849956/16769025\) | \(12518010086400\) | \([2, 2]\) | \(163840\) | \(1.2799\) | |
| 65520.ee4 | 65520bm1 | \([0, 0, 0, 393, -35786]\) | \(35969456/2985255\) | \(-557120229120\) | \([2]\) | \(81920\) | \(0.93333\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65520.ee have rank \(0\).
Complex multiplication
The elliptic curves in class 65520.ee do not have complex multiplication.Modular form 65520.2.a.ee
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
