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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 71478ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71478.u3 | 71478ba1 | \([1, -1, 0, -17937, 876649]\) | \(18609625/1188\) | \(40744179331812\) | \([2]\) | \(221184\) | \(1.3621\) | \(\Gamma_0(N)\)-optimal |
| 71478.u4 | 71478ba2 | \([1, -1, 0, 14553, 3677287]\) | \(9938375/176418\) | \(-6050510630774082\) | \([2]\) | \(442368\) | \(1.7087\) | |
| 71478.u1 | 71478ba3 | \([1, -1, 0, -261612, -51240560]\) | \(57736239625/255552\) | \(8764525687376448\) | \([2]\) | \(663552\) | \(1.9114\) | |
| 71478.u2 | 71478ba4 | \([1, -1, 0, -131652, -102262856]\) | \(-7357983625/127552392\) | \(-4374593883711769608\) | \([2]\) | \(1327104\) | \(2.2580\) |
Rank
sage: E.rank()
The elliptic curves in class 71478ba have rank \(0\).
Complex multiplication
The elliptic curves in class 71478ba do not have complex multiplication.Modular form 71478.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
