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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 18240b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18240.i3 | 18240b1 | \([0, -1, 0, -236, -1314]\) | \(22809653056/106875\) | \(6840000\) | \([2]\) | \(4096\) | \(0.16141\) | \(\Gamma_0(N)\)-optimal |
| 18240.i2 | 18240b2 | \([0, -1, 0, -361, 361]\) | \(1273760704/731025\) | \(2994278400\) | \([2, 2]\) | \(8192\) | \(0.50799\) | |
| 18240.i1 | 18240b3 | \([0, -1, 0, -4161, 104481]\) | \(243204324488/623295\) | \(20424130560\) | \([2]\) | \(16384\) | \(0.85456\) | |
| 18240.i4 | 18240b4 | \([0, -1, 0, 1439, 1441]\) | \(10049728312/5864445\) | \(-192166133760\) | \([2]\) | \(16384\) | \(0.85456\) |
Rank
sage: E.rank()
The elliptic curves in class 18240b have rank \(1\).
Complex multiplication
The elliptic curves in class 18240b do not have complex multiplication.Modular form 18240.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
