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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 630.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
630.i1 | 630j3 | \([1, -1, 1, -3362, -74181]\) | \(5763259856089/5670\) | \(4133430\) | \([2]\) | \(512\) | \(0.56289\) | |
630.i2 | 630j2 | \([1, -1, 1, -212, -1101]\) | \(1439069689/44100\) | \(32148900\) | \([2, 2]\) | \(256\) | \(0.21632\) | |
630.i3 | 630j1 | \([1, -1, 1, -32, 51]\) | \(4826809/1680\) | \(1224720\) | \([4]\) | \(128\) | \(-0.13026\) | \(\Gamma_0(N)\)-optimal |
630.i4 | 630j4 | \([1, -1, 1, 58, -3909]\) | \(30080231/9003750\) | \(-6563733750\) | \([2]\) | \(512\) | \(0.56289\) |
Rank
sage: E.rank()
The elliptic curves in class 630.i have rank \(0\).
Complex multiplication
The elliptic curves in class 630.i do not have complex multiplication.Modular form 630.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.