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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 207025w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207025.v2 | 207025w1 | \([1, 1, 1, -1660513, -897410844]\) | \(-9317\) | \(-54346862011736328125\) | \([]\) | \(3870720\) | \(2.5252\) | \(\Gamma_0(N)\)-optimal |
207025.v1 | 207025w2 | \([1, 1, 1, -43078387388, 3441398812632906]\) | \(-162677523113838677\) | \(-54346862011736328125\) | \([]\) | \(143216640\) | \(4.3306\) |
Rank
sage: E.rank()
The elliptic curves in class 207025w have rank \(0\).
Complex multiplication
The elliptic curves in class 207025w do not have complex multiplication.Modular form 207025.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.