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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 848b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
848.c2 | 848b1 | \([0, -1, 0, -4528, 150464]\) | \(-2507141976625/889192448\) | \(-3642132267008\) | \([]\) | \(1152\) | \(1.1212\) | \(\Gamma_0(N)\)-optimal |
848.c1 | 848b2 | \([0, -1, 0, -393648, 95194048]\) | \(-1646982616152408625/38112512\) | \(-156108849152\) | \([]\) | \(3456\) | \(1.6705\) |
Rank
sage: E.rank()
The elliptic curves in class 848b have rank \(0\).
Complex multiplication
The elliptic curves in class 848b do not have complex multiplication.Modular form 848.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.