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SageMath
E = EllipticCurve("ib1")
E.isogeny_class()
Elliptic curves in class 273600.ib
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.ib1 | 273600ib4 | \([0, 0, 0, -27360300, -55084498000]\) | \(3034301922374404/1425\) | \(1063756800000000\) | \([2]\) | \(6291456\) | \(2.6571\) | |
| 273600.ib2 | 273600ib3 | \([0, 0, 0, -2052300, -491722000]\) | \(1280615525284/601171875\) | \(448772400000000000000\) | \([2]\) | \(6291456\) | \(2.6571\) | |
| 273600.ib3 | 273600ib2 | \([0, 0, 0, -1710300, -860398000]\) | \(2964647793616/2030625\) | \(378963360000000000\) | \([2, 2]\) | \(3145728\) | \(2.3105\) | |
| 273600.ib4 | 273600ib1 | \([0, 0, 0, -85800, -18907000]\) | \(-5988775936/9774075\) | \(-114004810800000000\) | \([2]\) | \(1572864\) | \(1.9639\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.ib have rank \(0\).
Complex multiplication
The elliptic curves in class 273600.ib do not have complex multiplication.Modular form 273600.2.a.ib
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.
