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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 111090b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.a2 | 111090b1 | \([1, 1, 0, -2908188, 1895385552]\) | \(18374873741826841/136564270080\) | \(20216413126928901120\) | \([2]\) | \(3379200\) | \(2.5350\) | \(\Gamma_0(N)\)-optimal |
111090.a1 | 111090b2 | \([1, 1, 0, -4854908, -962788752]\) | \(85486955243540761/46777901234400\) | \(6924808194788601381600\) | \([2]\) | \(6758400\) | \(2.8815\) |
Rank
sage: E.rank()
The elliptic curves in class 111090b have rank \(0\).
Complex multiplication
The elliptic curves in class 111090b do not have complex multiplication.Modular form 111090.2.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.