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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 170352.eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170352.eu1 | 170352fj3 | \([0, 0, 0, -231699, 42872258]\) | \(381775972/567\) | \(2043010777586688\) | \([2]\) | \(1179648\) | \(1.8387\) | |
| 170352.eu2 | 170352fj2 | \([0, 0, 0, -18759, 241670]\) | \(810448/441\) | \(397252095641856\) | \([2, 2]\) | \(589824\) | \(1.4922\) | |
| 170352.eu3 | 170352fj1 | \([0, 0, 0, -11154, -450385]\) | \(2725888/21\) | \(1182297903696\) | \([2]\) | \(294912\) | \(1.1456\) | \(\Gamma_0(N)\)-optimal |
| 170352.eu4 | 170352fj4 | \([0, 0, 0, 72501, 1902602]\) | \(11696828/7203\) | \(-25953803581934592\) | \([2]\) | \(1179648\) | \(1.8387\) |
Rank
sage: E.rank()
The elliptic curves in class 170352.eu have rank \(2\).
Complex multiplication
The elliptic curves in class 170352.eu do not have complex multiplication.Modular form 170352.2.a.eu
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.
