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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 290400dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 290400.dx3 | 290400dx1 | \([0, 1, 0, -91758, -10333512]\) | \(48228544/2025\) | \(3587411025000000\) | \([2, 2]\) | \(2211840\) | \(1.7494\) | \(\Gamma_0(N)\)-optimal |
| 290400.dx2 | 290400dx2 | \([0, 1, 0, -243008, 32318988]\) | \(111980168/32805\) | \(464928468840000000\) | \([2]\) | \(4423680\) | \(2.0960\) | |
| 290400.dx4 | 290400dx3 | \([0, 1, 0, 44367, -38239137]\) | \(85184/5625\) | \(-637761960000000000\) | \([2]\) | \(4423680\) | \(2.0960\) | |
| 290400.dx1 | 290400dx4 | \([0, 1, 0, -1453008, -674623512]\) | \(23937672968/45\) | \(637761960000000\) | \([2]\) | \(4423680\) | \(2.0960\) |
Rank
sage: E.rank()
The elliptic curves in class 290400dx have rank \(0\).
Complex multiplication
The elliptic curves in class 290400dx do not have complex multiplication.Modular form 290400.2.a.dx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
