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SageMath
sage: E = EllipticCurve("f1")
sage: E.isogeny_class()
Elliptic curves in class 87120.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.f1 | 87120ew4 | \([0, 0, 0, -7732263, 8275761362]\) | \(154639330142416/33275\) | \(11001240747129600\) | \([2]\) | \(2488320\) | \(2.4627\) | |
| 87120.f2 | 87120ew3 | \([0, 0, 0, -484968, 128352323]\) | \(610462990336/8857805\) | \(183033142930368720\) | \([2]\) | \(1244160\) | \(2.1161\) | |
| 87120.f3 | 87120ew2 | \([0, 0, 0, -109263, 7855562]\) | \(436334416/171875\) | \(56824590636000000\) | \([2]\) | \(829440\) | \(1.9134\) | |
| 87120.f4 | 87120ew1 | \([0, 0, 0, -49368, -4135417]\) | \(643956736/15125\) | \(312535248498000\) | \([2]\) | \(414720\) | \(1.5668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.f have rank \(0\).
Complex multiplication
The elliptic curves in class 87120.f do not have complex multiplication.Modular form 87120.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
