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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 29744ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29744.z2 | 29744ba1 | \([0, 1, 0, 757064, -38628524]\) | \(2427173723519/1437646496\) | \(-28423147707233337344\) | \([]\) | \(483840\) | \(2.4222\) | \(\Gamma_0(N)\)-optimal |
| 29744.z1 | 29744ba2 | \([0, 1, 0, -75522776, 252654335636]\) | \(-2409558590804994721/674373039626\) | \(-13332766134370850545664\) | \([]\) | \(2419200\) | \(3.2269\) |
Rank
sage: E.rank()
The elliptic curves in class 29744ba have rank \(1\).
Complex multiplication
The elliptic curves in class 29744ba do not have complex multiplication.Modular form 29744.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
