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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 16016.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16016.e1 | 16016j4 | \([0, 0, 0, -158651, 24322730]\) | \(107818231938348177/4463459\) | \(18282328064\) | \([4]\) | \(38912\) | \(1.4554\) | |
| 16016.e2 | 16016j3 | \([0, 0, 0, -16091, -147254]\) | \(112489728522417/62811265517\) | \(257274943557632\) | \([2]\) | \(38912\) | \(1.4554\) | |
| 16016.e3 | 16016j2 | \([0, 0, 0, -9931, 378810]\) | \(26444947540257/169338169\) | \(693609140224\) | \([2, 2]\) | \(19456\) | \(1.1088\) | |
| 16016.e4 | 16016j1 | \([0, 0, 0, -251, 12906]\) | \(-426957777/17320303\) | \(-70943961088\) | \([2]\) | \(9728\) | \(0.76223\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16016.e have rank \(1\).
Complex multiplication
The elliptic curves in class 16016.e do not have complex multiplication.Modular form 16016.2.a.e
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.
