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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 205350dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 205350.h2 | 205350dx1 | \([1, 1, 0, -206030280770, -35995249158901260]\) | \(297688014855936424505245/433811768034816\) | \(1409473302934576474971035020800\) | \([]\) | \(1222776000\) | \(5.0552\) | \(\Gamma_0(N)\)-optimal |
| 205350.h1 | 205350dx2 | \([1, 1, 0, -1188201321575, 472656550966627125]\) | \(146176731012051803725/8549802417586176\) | \(10851046846617723360226836480000000000\) | \([]\) | \(6113880000\) | \(5.8599\) |
Rank
sage: E.rank()
The elliptic curves in class 205350dx have rank \(0\).
Complex multiplication
The elliptic curves in class 205350dx do not have complex multiplication.Modular form 205350.2.a.dx
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
