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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 85800b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85800.c2 | 85800b1 | \([0, -1, 0, 36592, 3334812]\) | \(338649393884/498444375\) | \(-7975110000000000\) | \([2]\) | \(663552\) | \(1.7367\) | \(\Gamma_0(N)\)-optimal |
| 85800.c1 | 85800b2 | \([0, -1, 0, -238408, 33584812]\) | \(46831495741058/11946352275\) | \(382283272800000000\) | \([2]\) | \(1327104\) | \(2.0833\) |
Rank
sage: E.rank()
The elliptic curves in class 85800b have rank \(1\).
Complex multiplication
The elliptic curves in class 85800b do not have complex multiplication.Modular form 85800.2.a.b
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.
