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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 75456.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75456.dg1 | 75456w1 | \([0, 0, 0, -40908, 3168880]\) | \(39616946929/226368\) | \(43259598471168\) | \([2]\) | \(442368\) | \(1.4580\) | \(\Gamma_0(N)\)-optimal |
| 75456.dg2 | 75456w2 | \([0, 0, 0, -17868, 6717040]\) | \(-3301293169/100082952\) | \(-19126149974065152\) | \([2]\) | \(884736\) | \(1.8046\) |
Rank
sage: E.rank()
The elliptic curves in class 75456.dg have rank \(0\).
Complex multiplication
The elliptic curves in class 75456.dg do not have complex multiplication.Modular form 75456.2.a.dg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
