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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 89280.em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.em1 | 89280by4 | \([0, 0, 0, -239052, -44984464]\) | \(15811147933922/1016955\) | \(97171563479040\) | \([2]\) | \(393216\) | \(1.7415\) | |
| 89280.em2 | 89280by3 | \([0, 0, 0, -80652, 8278256]\) | \(607199886722/41558445\) | \(3970971258716160\) | \([2]\) | \(393216\) | \(1.7415\) | |
| 89280.em3 | 89280by2 | \([0, 0, 0, -15852, -612304]\) | \(9220796644/1946025\) | \(92972792217600\) | \([2, 2]\) | \(196608\) | \(1.3949\) | |
| 89280.em4 | 89280by1 | \([0, 0, 0, 2148, -57904]\) | \(91765424/174375\) | \(-2082723840000\) | \([2]\) | \(98304\) | \(1.0483\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 89280.em have rank \(1\).
Complex multiplication
The elliptic curves in class 89280.em do not have complex multiplication.Modular form 89280.2.a.em
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.
