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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 350056b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350056.b2 | 350056b1 | \([0, 1, 0, -11870119, -15746288454]\) | \(-98260901558505084928/10035449471299\) | \(-18890569517581696816\) | \([2]\) | \(14017536\) | \(2.7319\) | \(\Gamma_0(N)\)-optimal |
350056.b1 | 350056b2 | \([0, 1, 0, -189926564, -1007520687104]\) | \(25156640481643577374288/262360721\) | \(7901817975021824\) | \([2]\) | \(28035072\) | \(3.0785\) |
Rank
sage: E.rank()
The elliptic curves in class 350056b have rank \(1\).
Complex multiplication
The elliptic curves in class 350056b do not have complex multiplication.Modular form 350056.2.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.