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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 235340d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235340.d2 | 235340d1 | \([0, -1, 0, -8965, -1600063]\) | \(-65536/875\) | \(-1064023349984000\) | \([]\) | \(846720\) | \(1.5650\) | \(\Gamma_0(N)\)-optimal |
235340.d1 | 235340d2 | \([0, -1, 0, -1353765, -605818703]\) | \(-225637236736/1715\) | \(-2085485765968640\) | \([]\) | \(2540160\) | \(2.1143\) |
Rank
sage: E.rank()
The elliptic curves in class 235340d have rank \(1\).
Complex multiplication
The elliptic curves in class 235340d do not have complex multiplication.Modular form 235340.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.