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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 32340.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32340.q1 | 32340p4 | \([0, -1, 0, -76260, 4428600]\) | \(1628514404944/664335375\) | \(20008548488544000\) | \([2]\) | \(248832\) | \(1.8256\) | |
| 32340.q2 | 32340p2 | \([0, -1, 0, -35100, -2519208]\) | \(158792223184/16335\) | \(491979882240\) | \([2]\) | \(82944\) | \(1.2763\) | |
| 32340.q3 | 32340p1 | \([0, -1, 0, -2025, -45198]\) | \(-488095744/200475\) | \(-377370932400\) | \([2]\) | \(41472\) | \(0.92968\) | \(\Gamma_0(N)\)-optimal |
| 32340.q4 | 32340p3 | \([0, -1, 0, 15615, 496350]\) | \(223673040896/187171875\) | \(-352329342750000\) | \([2]\) | \(124416\) | \(1.4790\) |
Rank
sage: E.rank()
The elliptic curves in class 32340.q have rank \(0\).
Complex multiplication
The elliptic curves in class 32340.q do not have complex multiplication.Modular form 32340.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
