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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 8400.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8400.d1 | 8400bh2 | \([0, -1, 0, -1750208, 891798912]\) | \(-14822892630025/42\) | \(-1680000000000\) | \([]\) | \(72000\) | \(2.0024\) | |
| 8400.d2 | 8400bh1 | \([0, -1, 0, 352, 175872]\) | \(46969655/130691232\) | \(-13382782156800\) | \([]\) | \(14400\) | \(1.1977\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8400.d have rank \(0\).
Complex multiplication
The elliptic curves in class 8400.d do not have complex multiplication.Modular form 8400.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
