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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 55440.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55440.dt1 | 55440ck1 | \([0, 0, 0, -432, 3159]\) | \(28311552/2695\) | \(848730960\) | \([2]\) | \(32256\) | \(0.45114\) | \(\Gamma_0(N)\)-optimal |
55440.dt2 | 55440ck2 | \([0, 0, 0, 513, 15066]\) | \(2963088/21175\) | \(-106697606400\) | \([2]\) | \(64512\) | \(0.79772\) |
Rank
sage: E.rank()
The elliptic curves in class 55440.dt have rank \(0\).
Complex multiplication
The elliptic curves in class 55440.dt do not have complex multiplication.Modular form 55440.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.