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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 361998.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361998.k1 | 361998k3 | \([1, -1, 0, -25098813, 48404327895]\) | \(496930471478093017/250614\) | \(881846448919254\) | \([2]\) | \(14450688\) | \(2.6367\) | |
361998.k2 | 361998k4 | \([1, -1, 0, -1888353, 426518379]\) | \(211634149400857/100188617802\) | \(352538073814001033322\) | \([2]\) | \(14450688\) | \(2.6367\) | |
361998.k3 | 361998k2 | \([1, -1, 0, -1568943, 756341145]\) | \(121382959848697/86155524\) | \(303159212550685764\) | \([2, 2]\) | \(7225344\) | \(2.2902\) | |
361998.k4 | 361998k1 | \([1, -1, 0, -78363, 16715349]\) | \(-15124197817/25469808\) | \(-89621727993867888\) | \([2]\) | \(3612672\) | \(1.9436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 361998.k have rank \(1\).
Complex multiplication
The elliptic curves in class 361998.k do not have complex multiplication.Modular form 361998.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.