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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 148120.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148120.i1 | 148120e2 | \([0, 1, 0, -15497760, -22899437600]\) | \(1357792998752738/38897700625\) | \(11792907657375192320000\) | \([2]\) | \(12976128\) | \(3.0134\) | |
148120.i2 | 148120e1 | \([0, 1, 0, -2272760, 810342400]\) | \(8564808605476/3081640625\) | \(467142051328400000000\) | \([2]\) | \(6488064\) | \(2.6668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148120.i have rank \(1\).
Complex multiplication
The elliptic curves in class 148120.i do not have complex multiplication.Modular form 148120.2.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.