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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2394k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2394.h3 | 2394k1 | \([1, -1, 1, -716, 6095]\) | \(55611739513/11440128\) | \(8339853312\) | \([4]\) | \(1536\) | \(0.61903\) | \(\Gamma_0(N)\)-optimal |
| 2394.h2 | 2394k2 | \([1, -1, 1, -3596, -76849]\) | \(7052482298233/499254336\) | \(363956410944\) | \([2, 2]\) | \(3072\) | \(0.96561\) | |
| 2394.h1 | 2394k3 | \([1, -1, 1, -56516, -5157169]\) | \(27384399945278713/153257496\) | \(111724714584\) | \([2]\) | \(6144\) | \(1.3122\) | |
| 2394.h4 | 2394k4 | \([1, -1, 1, 3244, -339505]\) | \(5180411077127/70976229912\) | \(-51741671605848\) | \([2]\) | \(6144\) | \(1.3122\) |
Rank
sage: E.rank()
The elliptic curves in class 2394k have rank \(1\).
Complex multiplication
The elliptic curves in class 2394k do not have complex multiplication.Modular form 2394.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
