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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 390390cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 390390.cb3 | 390390cb1 | \([1, 0, 1, -54253, -3722392]\) | \(3658671062929/880165440\) | \(4248390467280960\) | \([2]\) | \(3732480\) | \(1.7099\) | \(\Gamma_0(N)\)-optimal |
| 390390.cb4 | 390390cb2 | \([1, 0, 1, 128267, -23361544]\) | \(48351870250991/76871856600\) | \(-371045769283589400\) | \([2]\) | \(7464960\) | \(2.0565\) | |
| 390390.cb1 | 390390cb3 | \([1, 0, 1, -4100113, -3195863344]\) | \(1579250141304807889/41926500\) | \(202371207538500\) | \([2]\) | \(11197440\) | \(2.2592\) | |
| 390390.cb2 | 390390cb4 | \([1, 0, 1, -4095043, -3204159892]\) | \(-1573398910560073969/8138108343750\) | \(-39281094596587593750\) | \([2]\) | \(22394880\) | \(2.6058\) |
Rank
sage: E.rank()
The elliptic curves in class 390390cb have rank \(0\).
Complex multiplication
The elliptic curves in class 390390cb do not have complex multiplication.Modular form 390390.2.a.cb
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.
