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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 394944.ec
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
394944.ec1 | 394944ec1 | \([0, -1, 0, -7000737, -7070892255]\) | \(81706955619457/744505344\) | \(345751324386127773696\) | \([2]\) | \(25804800\) | \(2.7632\) | \(\Gamma_0(N)\)-optimal |
394944.ec2 | 394944ec2 | \([0, -1, 0, -2044577, -16893010143]\) | \(-2035346265217/264305213568\) | \(-122744421339297126285312\) | \([2]\) | \(51609600\) | \(3.1098\) |
Rank
sage: E.rank()
The elliptic curves in class 394944.ec have rank \(1\).
Complex multiplication
The elliptic curves in class 394944.ec do not have complex multiplication.Modular form 394944.2.a.ec
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.