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SageMath
E = EllipticCurve("in1")
E.isogeny_class()
Elliptic curves in class 187200.in
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.in1 | 187200mi3 | \([0, 0, 0, -749100, 249550000]\) | \(62275269892/39\) | \(29113344000000\) | \([2]\) | \(1048576\) | \(1.9037\) | |
| 187200.in2 | 187200mi2 | \([0, 0, 0, -47100, 3850000]\) | \(61918288/1521\) | \(283855104000000\) | \([2, 2]\) | \(524288\) | \(1.5571\) | |
| 187200.in3 | 187200mi1 | \([0, 0, 0, -6600, -119000]\) | \(2725888/1053\) | \(12282192000000\) | \([2]\) | \(262144\) | \(1.2106\) | \(\Gamma_0(N)\)-optimal |
| 187200.in4 | 187200mi4 | \([0, 0, 0, 6900, 12166000]\) | \(48668/85683\) | \(-63962016768000000\) | \([2]\) | \(1048576\) | \(1.9037\) |
Rank
sage: E.rank()
The elliptic curves in class 187200.in have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.in do not have complex multiplication.Modular form 187200.2.a.in
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
