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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 39600dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.e3 | 39600dm1 | \([0, 0, 0, -9300, 451375]\) | \(-488095744/200475\) | \(-36536568750000\) | \([2]\) | \(110592\) | \(1.3108\) | \(\Gamma_0(N)\)-optimal |
39600.e2 | 39600dm2 | \([0, 0, 0, -161175, 24903250]\) | \(158792223184/16335\) | \(47632860000000\) | \([2]\) | \(221184\) | \(1.6573\) | |
39600.e4 | 39600dm3 | \([0, 0, 0, 71700, -4935125]\) | \(223673040896/187171875\) | \(-34112074218750000\) | \([2]\) | \(331776\) | \(1.8601\) | |
39600.e1 | 39600dm4 | \([0, 0, 0, -350175, -43325750]\) | \(1628514404944/664335375\) | \(1937201953500000000\) | \([2]\) | \(663552\) | \(2.2066\) |
Rank
sage: E.rank()
The elliptic curves in class 39600dm have rank \(1\).
Complex multiplication
The elliptic curves in class 39600dm do not have complex multiplication.Modular form 39600.2.a.dm
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.