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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 11760.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11760.i1 | 11760bk2 | \([0, -1, 0, -160981, 24965725]\) | \(-19539165184/46875\) | \(-1106841792000000\) | \([]\) | \(72576\) | \(1.7660\) | |
11760.i2 | 11760bk1 | \([0, -1, 0, 3659, 170941]\) | \(229376/675\) | \(-15938521804800\) | \([]\) | \(24192\) | \(1.2167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11760.i have rank \(0\).
Complex multiplication
The elliptic curves in class 11760.i do not have complex multiplication.Modular form 11760.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.