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SageMath
E = EllipticCurve("ot1")
E.isogeny_class()
Elliptic curves in class 369600ot
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ot2 | 369600ot1 | \([0, 1, 0, -133, -34387]\) | \(-262144/509355\) | \(-509355000000\) | \([]\) | \(497664\) | \(0.92534\) | \(\Gamma_0(N)\)-optimal |
| 369600.ot1 | 369600ot2 | \([0, 1, 0, -84133, -9421387]\) | \(-65860951343104/3493875\) | \(-3493875000000\) | \([]\) | \(1492992\) | \(1.4746\) |
Rank
sage: E.rank()
The elliptic curves in class 369600ot have rank \(1\).
Complex multiplication
The elliptic curves in class 369600ot do not have complex multiplication.Modular form 369600.2.a.ot
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.
