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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 15210.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.d1 | 15210l2 | \([1, -1, 0, -692340, 239849936]\) | \(-1762712152495281/171798691840\) | \(-3577015237041192960\) | \([]\) | \(376320\) | \(2.3011\) | |
| 15210.d2 | 15210l1 | \([1, -1, 0, -7890, -437644]\) | \(-2609064081/2500000\) | \(-52052422500000\) | \([]\) | \(53760\) | \(1.3281\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15210.d have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.d do not have complex multiplication.Modular form 15210.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
