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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 159120.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.ca1 | 159120ca4 | \([0, 0, 0, -54332643, -154148452382]\) | \(5940441603429810927841/3044264109120\) | \(9090123921606574080\) | \([2]\) | \(14155776\) | \(2.9700\) | |
| 159120.ca2 | 159120ca2 | \([0, 0, 0, -3414243, -2381069342]\) | \(1474074790091785441/32813650022400\) | \(97981033948486041600\) | \([2, 2]\) | \(7077888\) | \(2.6234\) | |
| 159120.ca3 | 159120ca1 | \([0, 0, 0, -465123, 67290082]\) | \(3726830856733921/1501644718080\) | \(4483887101871390720\) | \([2]\) | \(3538944\) | \(2.2769\) | \(\Gamma_0(N)\)-optimal |
| 159120.ca4 | 159120ca3 | \([0, 0, 0, 318237, -7308689438]\) | \(1193680917131039/7728836230440000\) | \(-23078181322714152960000\) | \([2]\) | \(14155776\) | \(2.9700\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 159120.ca do not have complex multiplication.Modular form 159120.2.a.ca
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
