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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 200400t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200400.cr2 | 200400t1 | \([0, 1, 0, -592008, -756384012]\) | \(-358531401121921/3652290000000\) | \(-233746560000000000000\) | \([]\) | \(5419008\) | \(2.5906\) | \(\Gamma_0(N)\)-optimal |
| 200400.cr1 | 200400t2 | \([0, 1, 0, -152212008, 733807655988]\) | \(-6093832136609347161121/108676727597808690\) | \(-6955310566259756160000000\) | \([]\) | \(37933056\) | \(3.5636\) |
Rank
sage: E.rank()
The elliptic curves in class 200400t have rank \(1\).
Complex multiplication
The elliptic curves in class 200400t do not have complex multiplication.Modular form 200400.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
