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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 310464.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.di1 | 310464di2 | \([0, 0, 0, -6473772396, 200486093041584]\) | \(144106117295241933/247808\) | \(51597528211952618176512\) | \([2]\) | \(158957568\) | \(4.0471\) | |
| 310464.di2 | 310464di1 | \([0, 0, 0, -404483436, 3134665502640]\) | \(-35148950502093/46137344\) | \(-9606521616188996547772416\) | \([2]\) | \(79478784\) | \(3.7005\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.di have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.di do not have complex multiplication.Modular form 310464.2.a.di
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 LMFDB 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 LMFDB labels.
