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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 11760.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11760.bz1 | 11760ci2 | \([0, 1, 0, -73516, -4878616]\) | \(4253563312/1476225\) | \(15250176894355200\) | \([2]\) | \(107520\) | \(1.8069\) | |
11760.bz2 | 11760ci1 | \([0, 1, 0, -30641, 1998534]\) | \(4927700992/151875\) | \(98059265010000\) | \([2]\) | \(53760\) | \(1.4603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11760.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 11760.bz do not have complex multiplication.Modular form 11760.2.a.bz
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.