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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 70560.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.dd1 | 70560dv4 | \([0, 0, 0, -70707, -7236614]\) | \(890277128/15\) | \(658683809280\) | \([2]\) | \(196608\) | \(1.3981\) | |
| 70560.dd2 | 70560dv3 | \([0, 0, 0, -17787, 801934]\) | \(14172488/1875\) | \(82335476160000\) | \([2]\) | \(196608\) | \(1.3981\) | |
| 70560.dd3 | 70560dv1 | \([0, 0, 0, -4557, -105644]\) | \(1906624/225\) | \(1235032142400\) | \([2, 2]\) | \(98304\) | \(1.0515\) | \(\Gamma_0(N)\)-optimal |
| 70560.dd4 | 70560dv2 | \([0, 0, 0, 6468, -537824]\) | \(85184/405\) | \(-142275702804480\) | \([2]\) | \(196608\) | \(1.3981\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.dd have rank \(1\).
Complex multiplication
The elliptic curves in class 70560.dd do not have complex multiplication.Modular form 70560.2.a.dd
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
