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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2318.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2318.d1 | 2318e2 | \([1, 1, 1, -82015, -9074589]\) | \(-61010405398305333361/32094659438\) | \(-32094659438\) | \([]\) | \(8300\) | \(1.3466\) | |
2318.d2 | 2318e1 | \([1, 1, 1, 255, -2849]\) | \(1833318007919/4833345248\) | \(-4833345248\) | \([5]\) | \(1660\) | \(0.54192\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2318.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2318.d do not have complex multiplication.Modular form 2318.2.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.