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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 46800.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.dt1 | 46800ff1 | \([0, 0, 0, -3675, 87050]\) | \(-2941225/52\) | \(-97044480000\) | \([]\) | \(41472\) | \(0.90529\) | \(\Gamma_0(N)\)-optimal |
46800.dt2 | 46800ff2 | \([0, 0, 0, 14325, 414650]\) | \(174196775/140608\) | \(-262408273920000\) | \([]\) | \(124416\) | \(1.4546\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.dt do not have complex multiplication.Modular form 46800.2.a.dt
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.