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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 100016.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100016.i1 | 100016k2 | \([0, 0, 0, -89935, 10380666]\) | \(314246148685362000/13402725343\) | \(3431097687808\) | \([2]\) | \(253440\) | \(1.4848\) | |
100016.i2 | 100016k1 | \([0, 0, 0, -5900, 145203]\) | \(1419579648000000/252250397357\) | \(4036006357712\) | \([2]\) | \(126720\) | \(1.1383\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100016.i have rank \(1\).
Complex multiplication
The elliptic curves in class 100016.i do not have complex multiplication.Modular form 100016.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.