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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 303600g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 303600.g2 | 303600g1 | \([0, -1, 0, -307643128, -2075427471248]\) | \(6289200031265608678921133/4856126144979664896\) | \(2486336586229588426752000\) | \([2]\) | \(85155840\) | \(3.6128\) | \(\Gamma_0(N)\)-optimal |
| 303600.g1 | 303600g2 | \([0, -1, 0, -4921377528, -132884025180048]\) | \(25746239019564513863940330413/15367461154062336\) | \(7868140110879916032000\) | \([2]\) | \(170311680\) | \(3.9594\) |
Rank
sage: E.rank()
The elliptic curves in class 303600g have rank \(1\).
Complex multiplication
The elliptic curves in class 303600g do not have complex multiplication.Modular form 303600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
