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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2898.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2898.f1 | 2898e4 | \([1, -1, 0, -1609641, 786437127]\) | \(632678989847546725777/80515134\) | \(58695532686\) | \([2]\) | \(30720\) | \(1.9263\) | |
2898.f2 | 2898e3 | \([1, -1, 0, -115101, 8540235]\) | \(231331938231569617/90942310746882\) | \(66296944534476978\) | \([2]\) | \(30720\) | \(1.9263\) | |
2898.f3 | 2898e2 | \([1, -1, 0, -100611, 12304737]\) | \(154502321244119857/55101928644\) | \(40169305981476\) | \([2, 2]\) | \(15360\) | \(1.5797\) | |
2898.f4 | 2898e1 | \([1, -1, 0, -5391, 249885]\) | \(-23771111713777/22848457968\) | \(-16656525858672\) | \([2]\) | \(7680\) | \(1.2331\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2898.f have rank \(0\).
Complex multiplication
The elliptic curves in class 2898.f do not have complex multiplication.Modular form 2898.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.