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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 11088.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11088.v1 | 11088i2 | \([0, 0, 0, -4035, -97886]\) | \(4866277250/43659\) | \(65182537728\) | \([2]\) | \(12288\) | \(0.89787\) | |
11088.v2 | 11088i1 | \([0, 0, 0, -75, -3638]\) | \(-62500/7623\) | \(-5690539008\) | \([2]\) | \(6144\) | \(0.55130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.v have rank \(0\).
Complex multiplication
The elliptic curves in class 11088.v do not have complex multiplication.Modular form 11088.2.a.v
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 LMFDB 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 LMFDB labels.