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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 152460.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.k1 | 152460by2 | \([0, 0, 0, -1009503, -279805482]\) | \(12745567728/3587045\) | \(32020211318595413760\) | \([2]\) | \(3870720\) | \(2.4497\) | |
152460.k2 | 152460by1 | \([0, 0, 0, -927828, -343953027]\) | \(158328373248/21175\) | \(11813832393224400\) | \([2]\) | \(1935360\) | \(2.1031\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152460.k have rank \(1\).
Complex multiplication
The elliptic curves in class 152460.k do not have complex multiplication.Modular form 152460.2.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 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.