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SageMath
E = EllipticCurve("ro1")
E.isogeny_class()
Elliptic curves in class 369600ro
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ro3 | 369600ro1 | \([0, 1, 0, -325633, -71579137]\) | \(932288503609/779625\) | \(3193344000000000\) | \([2]\) | \(3538944\) | \(1.9029\) | \(\Gamma_0(N)\)-optimal |
| 369600.ro2 | 369600ro2 | \([0, 1, 0, -397633, -37667137]\) | \(1697509118089/833765625\) | \(3415104000000000000\) | \([2, 2]\) | \(7077888\) | \(2.2495\) | |
| 369600.ro1 | 369600ro3 | \([0, 1, 0, -3397633, 2383332863]\) | \(1058993490188089/13182390375\) | \(53995070976000000000\) | \([2]\) | \(14155776\) | \(2.5960\) | |
| 369600.ro4 | 369600ro4 | \([0, 1, 0, 1450367, -287147137]\) | \(82375335041831/56396484375\) | \(-231000000000000000000\) | \([2]\) | \(14155776\) | \(2.5960\) |
Rank
sage: E.rank()
The elliptic curves in class 369600ro have rank \(0\).
Complex multiplication
The elliptic curves in class 369600ro do not have complex multiplication.Modular form 369600.2.a.ro
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.
