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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 121275dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.dk2 | 121275dx1 | \([0, 0, 1, -14700, -39755844]\) | \(-262144/509355\) | \(-682584415030546875\) | \([]\) | \(1327104\) | \(2.1010\) | \(\Gamma_0(N)\)-optimal |
| 121275.dk1 | 121275dx2 | \([0, 0, 1, -9275700, -10873968219]\) | \(-65860951343104/3493875\) | \(-4682126656388671875\) | \([]\) | \(3981312\) | \(2.6503\) |
Rank
sage: E.rank()
The elliptic curves in class 121275dx have rank \(0\).
Complex multiplication
The elliptic curves in class 121275dx do not have complex multiplication.Modular form 121275.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
