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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 224400.di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.di1 | 224400fq2 | \([0, -1, 0, -74281008, 246438424512]\) | \(708234550511150304361/23696640000\) | \(1516584960000000000\) | \([2]\) | \(16220160\) | \(2.9882\) | |
224400.di2 | 224400fq1 | \([0, -1, 0, -4649008, 3840536512]\) | \(173629978755828841/1000026931200\) | \(64001723596800000000\) | \([2]\) | \(8110080\) | \(2.6416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.di have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.di do not have complex multiplication.Modular form 224400.2.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.