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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 69300.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69300.bz1 | 69300bv2 | \([0, 0, 0, -116175, -15214250]\) | \(59466754384/121275\) | \(353637900000000\) | \([2]\) | \(368640\) | \(1.6781\) | |
69300.bz2 | 69300bv1 | \([0, 0, 0, -4800, -401375]\) | \(-67108864/343035\) | \(-62518128750000\) | \([2]\) | \(184320\) | \(1.3315\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 69300.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 69300.bz do not have complex multiplication.Modular form 69300.2.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.