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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 17424u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.bx4 | 17424u1 | \([0, 0, 0, 726, -206305]\) | \(2048/891\) | \(-18411167366064\) | \([2]\) | \(46080\) | \(1.2244\) | \(\Gamma_0(N)\)-optimal |
| 17424.bx3 | 17424u2 | \([0, 0, 0, -48279, -3979690]\) | \(37642192/1089\) | \(360040606269696\) | \([2, 2]\) | \(92160\) | \(1.5710\) | |
| 17424.bx1 | 17424u3 | \([0, 0, 0, -767019, -258557398]\) | \(37736227588/33\) | \(43641285608448\) | \([2]\) | \(184320\) | \(1.9176\) | |
| 17424.bx2 | 17424u4 | \([0, 0, 0, -113619, 9101378]\) | \(122657188/43923\) | \(58086551144844288\) | \([2]\) | \(184320\) | \(1.9176\) |
Rank
sage: E.rank()
The elliptic curves in class 17424u have rank \(1\).
Complex multiplication
The elliptic curves in class 17424u do not have complex multiplication.Modular form 17424.2.a.u
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.
