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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 87120.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.cv1 | 87120bj4 | \([0, 0, 0, -8218683, 466677882]\) | \(46424454082884/26794860125\) | \(35435216471319384192000\) | \([2]\) | \(8847360\) | \(3.0164\) | |
| 87120.cv2 | 87120bj2 | \([0, 0, 0, -5496183, -4941840618]\) | \(55537159171536/228765625\) | \(75633530136516000000\) | \([2, 2]\) | \(4423680\) | \(2.6698\) | |
| 87120.cv3 | 87120bj1 | \([0, 0, 0, -5490738, -4952154537]\) | \(885956203616256/15125\) | \(312535248498000\) | \([2]\) | \(2211840\) | \(2.3232\) | \(\Gamma_0(N)\)-optimal |
| 87120.cv4 | 87120bj3 | \([0, 0, 0, -2860803, -9690268302]\) | \(-1957960715364/29541015625\) | \(-39066906062250000000000\) | \([2]\) | \(8847360\) | \(3.0164\) |
Rank
sage: E.rank()
The elliptic curves in class 87120.cv have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.cv do not have complex multiplication.Modular form 87120.2.a.cv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
