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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 146205g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 146205.h2 | 146205g1 | \([0, 0, 1, -4332, -104600]\) | \(2359296/125\) | \(476339545125\) | \([]\) | \(172368\) | \(0.99758\) | \(\Gamma_0(N)\)-optimal |
| 146205.h1 | 146205g2 | \([0, 0, 1, -58482, 5416895]\) | \(884736/5\) | \(125010550222605\) | \([]\) | \(517104\) | \(1.5469\) |
Rank
sage: E.rank()
The elliptic curves in class 146205g have rank \(1\).
Complex multiplication
The elliptic curves in class 146205g do not have complex multiplication.Modular form 146205.2.a.g
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.
