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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 63525.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63525.bg1 | 63525n2 | \([0, -1, 1, -8433, 300893]\) | \(35084566528/1029\) | \(1945453125\) | \([]\) | \(62208\) | \(0.88220\) | |
63525.bg2 | 63525n1 | \([0, -1, 1, -183, -232]\) | \(360448/189\) | \(357328125\) | \([]\) | \(20736\) | \(0.33290\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63525.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 63525.bg do not have complex multiplication.Modular form 63525.2.a.bg
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.