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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 87360ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.cg1 | 87360ev1 | \([0, -1, 0, -78625, 4021057]\) | \(820221748268836/369468094905\) | \(24213461067694080\) | \([2]\) | \(602112\) | \(1.8391\) | \(\Gamma_0(N)\)-optimal |
| 87360.cg2 | 87360ev2 | \([0, -1, 0, 272895, 29822625]\) | \(17147425715207422/12872524043925\) | \(-1687227471485337600\) | \([2]\) | \(1204224\) | \(2.1857\) |
Rank
sage: E.rank()
The elliptic curves in class 87360ev have rank \(1\).
Complex multiplication
The elliptic curves in class 87360ev do not have complex multiplication.Modular form 87360.2.a.ev
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
