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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 38025da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38025.d2 | 38025da1 | \([0, 0, 1, -164775, -25526394]\) | \(102400\) | \(4831675026823125\) | \([]\) | \(336960\) | \(1.8289\) | \(\Gamma_0(N)\)-optimal |
| 38025.d1 | 38025da2 | \([0, 0, 1, -9062625, 10500630156]\) | \(27258880\) | \(3019796891764453125\) | \([]\) | \(1684800\) | \(2.6336\) |
Rank
sage: E.rank()
The elliptic curves in class 38025da have rank \(0\).
Complex multiplication
The elliptic curves in class 38025da do not have complex multiplication.Modular form 38025.2.a.da
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
