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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 93600.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.d1 | 93600eq1 | \([0, 0, 0, -19425, 1042000]\) | \(1111934656/65\) | \(47385000000\) | \([2]\) | \(221184\) | \(1.1111\) | \(\Gamma_0(N)\)-optimal |
93600.d2 | 93600eq2 | \([0, 0, 0, -18300, 1168000]\) | \(-14526784/4225\) | \(-197121600000000\) | \([2]\) | \(442368\) | \(1.4577\) |
Rank
sage: E.rank()
The elliptic curves in class 93600.d have rank \(2\).
Complex multiplication
The elliptic curves in class 93600.d do not have complex multiplication.Modular form 93600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.