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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 10304k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10304.d2 | 10304k1 | \([0, 1, 0, 335, -1041]\) | \(253012016/181447\) | \(-2972827648\) | \([2]\) | \(7680\) | \(0.50613\) | \(\Gamma_0(N)\)-optimal |
10304.d1 | 10304k2 | \([0, 1, 0, -1505, -10241]\) | \(5756278756/2705927\) | \(177335631872\) | \([2]\) | \(15360\) | \(0.85271\) |
Rank
sage: E.rank()
The elliptic curves in class 10304k have rank \(2\).
Complex multiplication
The elliptic curves in class 10304k do not have complex multiplication.Modular form 10304.2.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.