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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 288990.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 288990.d1 | 288990d3 | \([1, -1, 0, -1876067595, 31277057797701]\) | \(207530301091125281552569/805586668007040\) | \(2834653061994550304077440\) | \([2]\) | \(165150720\) | \(3.9052\) | |
| 288990.d2 | 288990d4 | \([1, -1, 0, -355554315, -1992357222075]\) | \(1412712966892699019449/330160465517040000\) | \(1161750078166940139187440000\) | \([2]\) | \(165150720\) | \(3.9052\) | |
| 288990.d3 | 288990d2 | \([1, -1, 0, -119008395, 473350138821]\) | \(52974743974734147769/3152005008998400\) | \(11091097960053868858982400\) | \([2, 2]\) | \(82575360\) | \(3.5586\) | |
| 288990.d4 | 288990d1 | \([1, -1, 0, 5591925, 30545521605]\) | \(5495662324535111/117739817533440\) | \(-414296248367070408867840\) | \([2]\) | \(41287680\) | \(3.2120\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 288990.d have rank \(1\).
Complex multiplication
The elliptic curves in class 288990.d do not have complex multiplication.Modular form 288990.2.a.d
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.
