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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 97104bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97104.cs3 | 97104bb1 | \([0, 1, 0, -34487, -2476548]\) | \(11745974272/357\) | \(137873794128\) | \([2]\) | \(184320\) | \(1.2353\) | \(\Gamma_0(N)\)-optimal |
| 97104.cs2 | 97104bb2 | \([0, 1, 0, -35932, -2259220]\) | \(830321872/127449\) | \(787535112059136\) | \([2, 2]\) | \(368640\) | \(1.5819\) | |
| 97104.cs4 | 97104bb3 | \([0, 1, 0, 62328, -12360348]\) | \(1083360092/3306177\) | \(-81718349274842112\) | \([4]\) | \(737280\) | \(1.9285\) | |
| 97104.cs1 | 97104bb4 | \([0, 1, 0, -157312, 21774020]\) | \(17418812548/1753941\) | \(43351932835255296\) | \([2]\) | \(737280\) | \(1.9285\) |
Rank
sage: E.rank()
The elliptic curves in class 97104bb have rank \(1\).
Complex multiplication
The elliptic curves in class 97104bb do not have complex multiplication.Modular form 97104.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
