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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 148720i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148720.u1 | 148720i1 | \([0, -1, 0, -2760, -151568]\) | \(-117649/440\) | \(-8699068252160\) | \([]\) | \(221184\) | \(1.1685\) | \(\Gamma_0(N)\)-optimal |
148720.u2 | 148720i2 | \([0, -1, 0, 24280, 3612400]\) | \(80062991/332750\) | \(-6578670365696000\) | \([]\) | \(663552\) | \(1.7178\) |
Rank
sage: E.rank()
The elliptic curves in class 148720i have rank \(1\).
Complex multiplication
The elliptic curves in class 148720i do not have complex multiplication.Modular form 148720.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.