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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 18240.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18240.d1 | 18240d2 | \([0, -1, 0, -10241, -395295]\) | \(3625294417928/2193075\) | \(71862681600\) | \([2]\) | \(25600\) | \(1.0266\) | |
18240.d2 | 18240d1 | \([0, -1, 0, -521, -8439]\) | \(-3825694144/5609655\) | \(-22977146880\) | \([2]\) | \(12800\) | \(0.68005\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18240.d have rank \(1\).
Complex multiplication
The elliptic curves in class 18240.d do not have complex multiplication.Modular form 18240.2.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.