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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 7436.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7436.d1 | 7436c2 | \([0, 1, 0, -13069, -582737]\) | \(-199794688/1331\) | \(-1644667591424\) | \([]\) | \(12960\) | \(1.1795\) | |
| 7436.d2 | 7436c1 | \([0, 1, 0, 451, -4081]\) | \(8192/11\) | \(-13592294144\) | \([]\) | \(4320\) | \(0.63018\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7436.d have rank \(1\).
Complex multiplication
The elliptic curves in class 7436.d do not have complex multiplication.Modular form 7436.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
