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SageMath
E = EllipticCurve("ox1")
E.isogeny_class()
Elliptic curves in class 176400ox
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.je4 | 176400ox1 | \([0, 0, 0, 95550, 93853375]\) | \(4499456/180075\) | \(-3861083559768750000\) | \([2]\) | \(2359296\) | \(2.2463\) | \(\Gamma_0(N)\)-optimal |
| 176400.je3 | 176400ox2 | \([0, 0, 0, -2605575, 1549759750]\) | \(5702413264/275625\) | \(94557148402500000000\) | \([2, 2]\) | \(4718592\) | \(2.5929\) | |
| 176400.je1 | 176400ox3 | \([0, 0, 0, -41193075, 101761497250]\) | \(5633270409316/14175\) | \(19451756242800000000\) | \([2]\) | \(9437184\) | \(2.9395\) | |
| 176400.je2 | 176400ox4 | \([0, 0, 0, -7236075, -5483969750]\) | \(30534944836/8203125\) | \(11256803381250000000000\) | \([2]\) | \(9437184\) | \(2.9395\) |
Rank
sage: E.rank()
The elliptic curves in class 176400ox have rank \(1\).
Complex multiplication
The elliptic curves in class 176400ox do not have complex multiplication.Modular form 176400.2.a.ox
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.
