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SageMath
E = EllipticCurve("hf1")
E.isogeny_class()
Elliptic curves in class 203280hf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.m3 | 203280hf1 | \([0, -1, 0, -139916, -20097504]\) | \(667932971344/3465\) | \(1571445469440\) | \([2]\) | \(737280\) | \(1.5368\) | \(\Gamma_0(N)\)-optimal |
| 203280.m2 | 203280hf2 | \([0, -1, 0, -142336, -19363760]\) | \(175798419556/12006225\) | \(21780234206438400\) | \([2, 2]\) | \(1474560\) | \(1.8834\) | |
| 203280.m1 | 203280hf3 | \([0, -1, 0, -447256, 91871056]\) | \(2727138195938/576489375\) | \(2091593919824640000\) | \([2]\) | \(2949120\) | \(2.2300\) | |
| 203280.m4 | 203280hf4 | \([0, -1, 0, 123864, -83677680]\) | \(57925453822/866412855\) | \(-3143481802376509440\) | \([2]\) | \(2949120\) | \(2.2300\) |
Rank
sage: E.rank()
The elliptic curves in class 203280hf have rank \(0\).
Complex multiplication
The elliptic curves in class 203280hf do not have complex multiplication.Modular form 203280.2.a.hf
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.
