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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 95370.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.d1 | 95370j2 | \([1, 1, 0, -3193, -68987]\) | \(733138807913/21780000\) | \(107005140000\) | \([2]\) | \(163840\) | \(0.89329\) | |
95370.d2 | 95370j1 | \([1, 1, 0, -473, 2277]\) | \(2389979753/844800\) | \(4150502400\) | \([2]\) | \(81920\) | \(0.54671\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95370.d have rank \(2\).
Complex multiplication
The elliptic curves in class 95370.d do not have complex multiplication.Modular form 95370.2.a.d
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.