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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 346560.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.di1 | 346560di2 | \([0, -1, 0, -46173825, 120524330625]\) | \(882774443450089/2166000000\) | \(26712834898919424000000\) | \([2]\) | \(46448640\) | \(3.1815\) | |
| 346560.di2 | 346560di1 | \([0, -1, 0, -1814145, 3299440257]\) | \(-53540005609/350208000\) | \(-4319043621551603712000\) | \([2]\) | \(23224320\) | \(2.8349\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.di have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.di do not have complex multiplication.Modular form 346560.2.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.
