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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 24882.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.i1 | 24882i4 | \([1, 1, 0, -3496284, 2512999632]\) | \(4726547366169309395080393/3954322686107659008\) | \(3954322686107659008\) | \([4]\) | \(1048576\) | \(2.4963\) | |
24882.i2 | 24882i3 | \([1, 1, 0, -2280284, -1311976752]\) | \(1311266087944014056584393/16316901430937572608\) | \(16316901430937572608\) | \([2]\) | \(1048576\) | \(2.4963\) | |
24882.i3 | 24882i2 | \([1, 1, 0, -266844, 20517840]\) | \(2101350905468349310153/1032219066698366976\) | \(1032219066698366976\) | \([2, 2]\) | \(524288\) | \(2.1498\) | |
24882.i4 | 24882i1 | \([1, 1, 0, 60836, 2495440]\) | \(24899722750535932727/17045346513321984\) | \(-17045346513321984\) | \([2]\) | \(262144\) | \(1.8032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24882.i have rank \(0\).
Complex multiplication
The elliptic curves in class 24882.i do not have complex multiplication.Modular form 24882.2.a.i
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.