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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 439824.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439824.el1 | 439824el1 | \([0, 1, 0, -155248, 23491796]\) | \(858729462625/38148\) | \(18383151316992\) | \([2]\) | \(2211840\) | \(1.6225\) | \(\Gamma_0(N)\)-optimal |
439824.el2 | 439824el2 | \([0, 1, 0, -147408, 25978644]\) | \(-735091890625/181908738\) | \(-87660057055076352\) | \([2]\) | \(4423680\) | \(1.9691\) |
Rank
sage: E.rank()
The elliptic curves in class 439824.el have rank \(1\).
Complex multiplication
The elliptic curves in class 439824.el do not have complex multiplication.Modular form 439824.2.a.el
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.