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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 47040.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.q1 | 47040eg4 | \([0, -1, 0, -42401, -3344319]\) | \(546718898/405\) | \(6245298339840\) | \([2]\) | \(147456\) | \(1.3889\) | |
| 47040.q2 | 47040eg3 | \([0, -1, 0, -26721, 1670145]\) | \(136835858/1875\) | \(28913418240000\) | \([2]\) | \(147456\) | \(1.3889\) | |
| 47040.q3 | 47040eg2 | \([0, -1, 0, -3201, -27999]\) | \(470596/225\) | \(1734805094400\) | \([2, 2]\) | \(73728\) | \(1.0424\) | |
| 47040.q4 | 47040eg1 | \([0, -1, 0, 719, -3695]\) | \(21296/15\) | \(-28913418240\) | \([2]\) | \(36864\) | \(0.69578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47040.q have rank \(1\).
Complex multiplication
The elliptic curves in class 47040.q do not have complex multiplication.Modular form 47040.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
