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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 784.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
784.i1 | 784e2 | \([0, -1, 0, -1976, -32752]\) | \(3543122/49\) | \(11806312448\) | \([2]\) | \(768\) | \(0.73829\) | |
784.i2 | 784e1 | \([0, -1, 0, -16, -1392]\) | \(-4/7\) | \(-843308032\) | \([2]\) | \(384\) | \(0.39171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 784.i have rank \(0\).
Complex multiplication
The elliptic curves in class 784.i do not have complex multiplication.Modular form 784.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.