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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 96600k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96600.t1 | 96600k1 | \([0, -1, 0, -57384908, 167336029812]\) | \(5224645130090610708304/67370009765625\) | \(269480039062500000000\) | \([2]\) | \(10321920\) | \(3.0654\) | \(\Gamma_0(N)\)-optimal |
96600.t2 | 96600k2 | \([0, -1, 0, -55822408, 176876654812]\) | \(-1202345928696155427076/148724718496003125\) | \(-2379595495936050000000000\) | \([2]\) | \(20643840\) | \(3.4120\) |
Rank
sage: E.rank()
The elliptic curves in class 96600k have rank \(0\).
Complex multiplication
The elliptic curves in class 96600k do not have complex multiplication.Modular form 96600.2.a.k
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.