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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 334620o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
334620.o2 | 334620o1 | \([0, 0, 0, -184548, 10653253]\) | \(73056256/37125\) | \(353232611191746000\) | \([]\) | \(3234816\) | \(2.0596\) | \(\Gamma_0(N)\)-optimal |
334620.o1 | 334620o2 | \([0, 0, 0, -12048348, 16096779673]\) | \(20328806957056/19965\) | \(189960648685338960\) | \([3]\) | \(9704448\) | \(2.6089\) |
Rank
sage: E.rank()
The elliptic curves in class 334620o have rank \(2\).
Complex multiplication
The elliptic curves in class 334620o do not have complex multiplication.Modular form 334620.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.