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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 70560dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.g3 | 70560dn1 | \([0, 0, 0, -5733, 111132]\) | \(3796416/1225\) | \(6724063886400\) | \([2, 2]\) | \(147456\) | \(1.1649\) | \(\Gamma_0(N)\)-optimal |
| 70560.g4 | 70560dn2 | \([0, 0, 0, 16317, 759402]\) | \(10941048/12005\) | \(-527166608693760\) | \([2]\) | \(294912\) | \(1.5114\) | |
| 70560.g2 | 70560dn3 | \([0, 0, 0, -36603, -2611602]\) | \(123505992/4375\) | \(192116111040000\) | \([2]\) | \(294912\) | \(1.5114\) | |
| 70560.g1 | 70560dn4 | \([0, 0, 0, -82908, 9186912]\) | \(179406144/35\) | \(12295431106560\) | \([2]\) | \(294912\) | \(1.5114\) |
Rank
sage: E.rank()
The elliptic curves in class 70560dn have rank \(0\).
Complex multiplication
The elliptic curves in class 70560dn do not have complex multiplication.Modular form 70560.2.a.dn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
