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SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 364650.es
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.es1 | 364650es1 | \([1, 1, 1, -16015338, 24762647031]\) | \(-29074483888194524965849/137067820375749120\) | \(-2141684693371080000000\) | \([]\) | \(39191040\) | \(2.9429\) | \(\Gamma_0(N)\)-optimal |
364650.es2 | 364650es2 | \([1, 1, 1, 39184287, 131319344031]\) | \(425833213220888977995191/723096113321607168000\) | \(-11298376770650112000000000\) | \([]\) | \(117573120\) | \(3.4922\) |
Rank
sage: E.rank()
The elliptic curves in class 364650.es have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.es do not have complex multiplication.Modular form 364650.2.a.es
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.