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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 37440dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.t2 | 37440dc1 | \([0, 0, 0, -1548, 26128]\) | \(-57960603/8125\) | \(-57507840000\) | \([2]\) | \(32768\) | \(0.79593\) | \(\Gamma_0(N)\)-optimal |
37440.t1 | 37440dc2 | \([0, 0, 0, -25548, 1571728]\) | \(260549802603/4225\) | \(29904076800\) | \([2]\) | \(65536\) | \(1.1425\) |
Rank
sage: E.rank()
The elliptic curves in class 37440dc have rank \(1\).
Complex multiplication
The elliptic curves in class 37440dc do not have complex multiplication.Modular form 37440.2.a.dc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.