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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 126350.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126350.e1 | 126350h1 | \([1, 0, 1, -63513626, 145684403148]\) | \(5619814620139/1433600000\) | \(7228204430249600000000000\) | \([2]\) | \(26265600\) | \(3.4795\) | \(\Gamma_0(N)\)-optimal |
126350.e2 | 126350h2 | \([1, 0, 1, 155974374, 931451443148]\) | \(83230218613781/122500000000\) | \(-617644421530117187500000000\) | \([2]\) | \(52531200\) | \(3.8261\) |
Rank
sage: E.rank()
The elliptic curves in class 126350.e have rank \(1\).
Complex multiplication
The elliptic curves in class 126350.e do not have complex multiplication.Modular form 126350.2.a.e
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.