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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 372645.dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 372645.dh1 | 372645dh1 | \([0, 0, 1, -347802, -79313348]\) | \(-303464448/1625\) | \(-24915263433298875\) | \([]\) | \(3048192\) | \(1.9907\) | \(\Gamma_0(N)\)-optimal |
| 372645.dh2 | 372645dh2 | \([0, 0, 1, 894348, -422188153]\) | \(7077888/10985\) | \(-122783414809834187955\) | \([]\) | \(9144576\) | \(2.5400\) |
Rank
sage: E.rank()
The elliptic curves in class 372645.dh have rank \(1\).
Complex multiplication
The elliptic curves in class 372645.dh do not have complex multiplication.Modular form 372645.2.a.dh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
