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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 158400.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.q1 | 158400ci3 | \([0, 0, 0, -324300, 70958000]\) | \(10105715528/20625\) | \(7698240000000000\) | \([2]\) | \(1179648\) | \(1.9348\) | |
| 158400.q2 | 158400ci2 | \([0, 0, 0, -27300, 272000]\) | \(48228544/27225\) | \(1270209600000000\) | \([2, 2]\) | \(589824\) | \(1.5882\) | |
| 158400.q3 | 158400ci1 | \([0, 0, 0, -17175, -862000]\) | \(768575296/4455\) | \(3247695000000\) | \([2]\) | \(294912\) | \(1.2416\) | \(\Gamma_0(N)\)-optimal |
| 158400.q4 | 158400ci4 | \([0, 0, 0, 107700, 2162000]\) | \(370146232/219615\) | \(-81970859520000000\) | \([2]\) | \(1179648\) | \(1.9348\) |
Rank
sage: E.rank()
The elliptic curves in class 158400.q have rank \(1\).
Complex multiplication
The elliptic curves in class 158400.q do not have complex multiplication.Modular form 158400.2.a.q
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.
