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SageMath
E = EllipticCurve("mf1")
E.isogeny_class()
Elliptic curves in class 141120.mf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.mf1 | 141120bf3 | \([0, 0, 0, -4262412, 3386606384]\) | \(3047363673992/540225\) | \(1518239833038028800\) | \([2]\) | \(3145728\) | \(2.4933\) | |
| 141120.mf2 | 141120bf2 | \([0, 0, 0, -293412, 41533184]\) | \(7952095936/2480625\) | \(871438679677440000\) | \([2, 2]\) | \(1572864\) | \(2.1467\) | |
| 141120.mf3 | 141120bf1 | \([0, 0, 0, -114807, -14477344]\) | \(30488290624/1148175\) | \(6302369022667200\) | \([2]\) | \(786432\) | \(1.8002\) | \(\Gamma_0(N)\)-optimal |
| 141120.mf4 | 141120bf4 | \([0, 0, 0, 817908, 281133776]\) | \(21531355768/24609375\) | \(-69161799974400000000\) | \([2]\) | \(3145728\) | \(2.4933\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.mf have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.mf do not have complex multiplication.Modular form 141120.2.a.mf
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
