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SageMath
E = EllipticCurve("ma1")
E.isogeny_class()
Elliptic curves in class 158400ma
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.hk4 | 158400ma1 | \([0, 0, 0, 11700, -378000]\) | \(59319/55\) | \(-164229120000000\) | \([2]\) | \(393216\) | \(1.4149\) | \(\Gamma_0(N)\)-optimal |
| 158400.hk3 | 158400ma2 | \([0, 0, 0, -60300, -3402000]\) | \(8120601/3025\) | \(9032601600000000\) | \([2, 2]\) | \(786432\) | \(1.7615\) | |
| 158400.hk2 | 158400ma3 | \([0, 0, 0, -420300, 102438000]\) | \(2749884201/73205\) | \(218588958720000000\) | \([2]\) | \(1572864\) | \(2.1081\) | |
| 158400.hk1 | 158400ma4 | \([0, 0, 0, -852300, -302778000]\) | \(22930509321/6875\) | \(20528640000000000\) | \([2]\) | \(1572864\) | \(2.1081\) |
Rank
sage: E.rank()
The elliptic curves in class 158400ma have rank \(0\).
Complex multiplication
The elliptic curves in class 158400ma do not have complex multiplication.Modular form 158400.2.a.ma
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.
