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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 145040g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145040.k3 | 145040g1 | \([0, 1, 0, -58816, -3021516]\) | \(46694890801/18944000\) | \(9128929918976000\) | \([2]\) | \(829440\) | \(1.7603\) | \(\Gamma_0(N)\)-optimal |
145040.k4 | 145040g2 | \([0, 1, 0, 192064, -21787340]\) | \(1625964918479/1369000000\) | \(-659707826176000000\) | \([2]\) | \(1658880\) | \(2.1069\) | |
145040.k1 | 145040g3 | \([0, 1, 0, -4135616, -3238495436]\) | \(16232905099479601/4052240\) | \(1952735165480960\) | \([2]\) | \(2488320\) | \(2.3096\) | |
145040.k2 | 145040g4 | \([0, 1, 0, -4119936, -3264254540]\) | \(-16048965315233521/256572640900\) | \(-123639867921383833600\) | \([2]\) | \(4976640\) | \(2.6562\) |
Rank
sage: E.rank()
The elliptic curves in class 145040g have rank \(0\).
Complex multiplication
The elliptic curves in class 145040g do not have complex multiplication.Modular form 145040.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.