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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 162450.ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.ey1 | 162450bv4 | \([1, -1, 1, -78586880, -268073236753]\) | \(100162392144121/23457780\) | \(12570601786697612812500\) | \([2]\) | \(35389440\) | \(3.2309\) | |
| 162450.ey2 | 162450bv3 | \([1, -1, 1, -36349880, 82039003247]\) | \(9912050027641/311647500\) | \(167006281938011367187500\) | \([2]\) | \(35389440\) | \(3.2309\) | |
| 162450.ey3 | 162450bv2 | \([1, -1, 1, -5484380, -3149776753]\) | \(34043726521/11696400\) | \(6267890087550056250000\) | \([2, 2]\) | \(17694720\) | \(2.8844\) | |
| 162450.ey4 | 162450bv1 | \([1, -1, 1, 1013620, -342640753]\) | \(214921799/218880\) | \(-117293849591580000000\) | \([2]\) | \(8847360\) | \(2.5378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162450.ey have rank \(0\).
Complex multiplication
The elliptic curves in class 162450.ey do not have complex multiplication.Modular form 162450.2.a.ey
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.
