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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 354025k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
354025.k2 | 354025k1 | \([1, 1, 1, -113583, -16089494]\) | \(-9317\) | \(-17393535238596125\) | \([]\) | \(1720320\) | \(1.8546\) | \(\Gamma_0(N)\)-optimal |
354025.k1 | 354025k2 | \([1, 1, 1, -2946663658, 61565201177556]\) | \(-162677523113838677\) | \(-17393535238596125\) | \([]\) | \(63651840\) | \(3.6600\) |
Rank
sage: E.rank()
The elliptic curves in class 354025k have rank \(2\).
Complex multiplication
The elliptic curves in class 354025k do not have complex multiplication.Modular form 354025.2.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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.