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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 28314b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28314.g2 | 28314b1 | \([1, -1, 0, -138, -544]\) | \(8120601/676\) | \(24293412\) | \([2]\) | \(7680\) | \(0.15921\) | \(\Gamma_0(N)\)-optimal |
28314.g1 | 28314b2 | \([1, -1, 0, -468, 3350]\) | \(315821241/57122\) | \(2052793314\) | \([2]\) | \(15360\) | \(0.50578\) |
Rank
sage: E.rank()
The elliptic curves in class 28314b have rank \(2\).
Complex multiplication
The elliptic curves in class 28314b do not have complex multiplication.Modular form 28314.2.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.