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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 154800dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154800.m2 | 154800dx1 | \([0, 0, 0, -27675, 74250]\) | \(1860867/1075\) | \(1354190400000000\) | \([2]\) | \(589824\) | \(1.5930\) | \(\Gamma_0(N)\)-optimal |
| 154800.m1 | 154800dx2 | \([0, 0, 0, -297675, -62295750]\) | \(2315685267/9245\) | \(11646037440000000\) | \([2]\) | \(1179648\) | \(1.9396\) |
Rank
sage: E.rank()
The elliptic curves in class 154800dx have rank \(2\).
Complex multiplication
The elliptic curves in class 154800dx do not have complex multiplication.Modular form 154800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
