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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 37440ek
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.s2 | 37440ek1 | \([0, 0, 0, -70788, -8731712]\) | \(-13137573612736/3427734375\) | \(-10235160000000000\) | \([2]\) | \(184320\) | \(1.7890\) | \(\Gamma_0(N)\)-optimal |
| 37440.s1 | 37440ek2 | \([0, 0, 0, -1195788, -503281712]\) | \(7916055336451592/385003125\) | \(9196905369600000\) | \([2]\) | \(368640\) | \(2.1356\) |
Rank
sage: E.rank()
The elliptic curves in class 37440ek have rank \(0\).
Complex multiplication
The elliptic curves in class 37440ek do not have complex multiplication.Modular form 37440.2.a.ek
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.
