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SageMath
E = EllipticCurve("ob1")
E.isogeny_class()
Elliptic curves in class 141120.ob
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.ob1 | 141120op2 | \([0, 0, 0, -216972, -38673936]\) | \(3721734/25\) | \(7588037482905600\) | \([2]\) | \(1105920\) | \(1.8818\) | |
141120.ob2 | 141120op1 | \([0, 0, 0, -5292, -1333584]\) | \(-108/5\) | \(-758803748290560\) | \([2]\) | \(552960\) | \(1.5353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.ob have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.ob do not have complex multiplication.Modular form 141120.2.a.ob
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.