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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 277200b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.b1 | 277200b1 | \([0, 0, 0, -7732800, 8276623875]\) | \(10392086293512192/1684375\) | \(8288388281250000\) | \([2]\) | \(7188480\) | \(2.4564\) | \(\Gamma_0(N)\)-optimal |
277200.b2 | 277200b2 | \([0, 0, 0, -7709175, 8329709250]\) | \(-643570518871152/8271484375\) | \(-651230507812500000000\) | \([2]\) | \(14376960\) | \(2.8030\) |
Rank
sage: E.rank()
The elliptic curves in class 277200b have rank \(0\).
Complex multiplication
The elliptic curves in class 277200b do not have complex multiplication.Modular form 277200.2.a.b
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 Cremona 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 Cremona labels.