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SageMath
E = EllipticCurve("lc1")
E.isogeny_class()
Elliptic curves in class 141120.lc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.lc1 | 141120gc2 | \([0, 0, 0, -96012, 8192016]\) | \(55306341/15625\) | \(27653197824000000\) | \([2]\) | \(1179648\) | \(1.8617\) | |
141120.lc2 | 141120gc1 | \([0, 0, 0, -35532, -2476656]\) | \(2803221/125\) | \(221225582592000\) | \([2]\) | \(589824\) | \(1.5152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.lc have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.lc do not have complex multiplication.Modular form 141120.2.a.lc
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.