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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 115920.du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.du1 | 115920bl1 | \([0, 0, 0, -20658567, 36140450726]\) | \(5224645130090610708304/67370009765625\) | \(12572860702500000000\) | \([2]\) | \(6881280\) | \(2.8100\) | \(\Gamma_0(N)\)-optimal |
| 115920.du2 | 115920bl2 | \([0, 0, 0, -20096067, 38201338226]\) | \(-1202345928696155427076/148724718496003125\) | \(-111022407458392348800000\) | \([2]\) | \(13762560\) | \(3.1566\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.du have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.du do not have complex multiplication.Modular form 115920.2.a.du
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
