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SageMath
E = EllipticCurve("lk1")
E.isogeny_class()
Elliptic curves in class 418950lk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.lk2 | 418950lk1 | \([1, -1, 1, 98995, -8309003]\) | \(2161700757/1848320\) | \(-91737984240000000\) | \([2]\) | \(5529600\) | \(1.9424\) | \(\Gamma_0(N)\)-optimal* |
418950.lk1 | 418950lk2 | \([1, -1, 1, -489005, -72989003]\) | \(260549802603/104256800\) | \(5174595673537500000\) | \([2]\) | \(11059200\) | \(2.2890\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950lk have rank \(1\).
Complex multiplication
The elliptic curves in class 418950lk do not have complex multiplication.Modular form 418950.2.a.lk
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.