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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 85698h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85698.l1 | 85698h1 | \([1, -1, 0, -3273, -77887]\) | \(-35937/4\) | \(-431672652324\) | \([]\) | \(152064\) | \(0.96994\) | \(\Gamma_0(N)\)-optimal |
| 85698.l2 | 85698h2 | \([1, -1, 0, 20532, 107792]\) | \(109503/64\) | \(-559447757411904\) | \([]\) | \(456192\) | \(1.5192\) |
Rank
sage: E.rank()
The elliptic curves in class 85698h have rank \(0\).
Complex multiplication
The elliptic curves in class 85698h do not have complex multiplication.Modular form 85698.2.a.h
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
